According to the Noumea Accord New Caledonia too will hold a referendum regarding its independence from France between 2014 and 2019. http://en.wikipedia.org/wiki/Noumea_Accord
This will of course affect the WHS located there.
And of course there is the Scottish Independence Referendum planned for 2014.
http://en.wikipedia.org/wiki/Scotland_independence_referendum#2011_SNP_administration

I wonder what would happen to the Forth Bridge nomination, made in early 2014 for potential inscription in 2015, in the event of a majority Yes vote!?

A report of late improvements in the representation of non represented states:

First provided T-lists:
St Vincent, Sierra Leone.

First sites proposed:
Qatar, Lesotho, Guinea Bissau, Fiji.

First site inscribed as a transnational site:
Congo (Rep).

First sites inscribed:
Chad, Palau, Palestine.

This leaves us with the following list:

Not in Unesco:
Liechtenstein, Kosovo, Northern Cyprus, Taiwan, Western Sahara, Transnistria, Abkhazia, South Ossetia, Somaliland, Azawad, Nagorno-Karabakh.

Unesco members which didn't sign the WH convention:
Bahamas, South Sudan, Somalia, Singapore, Timor Leste, Tuvalu, Nauru.

Member states with no T-list:
Sao Tome, Equatorial Guinea, Kuwait, Niue, Cook Islands, Djibouti, Liberia, Rwanda, Brunei, Monaco.

Member states with T-list but no sites proposed:
Angola, Namibia, Eritrea, Swaziland, Burundi, Comoros, Maldives, Tonga, Samoa, Bhutan, Trinidad Tobago, Antigua Barbuda, Grenada, St Vincent, Sierra Leone.

Member states with sites proposed but not inscribed:
Lesotho, Myanmar, Micronesia, Qatar, Jamaica, Guyana, Guinea Bissau, Fiji.

Member states with only trans-national sites inscribed:
Zambia, Moldova, Guinea, Congo (Rep).

I found this list particularly interesting. It sometimes seems that countries get given an "easy ride" with their first nomination but here are some which have tried and failed. And in some cases it hasn't just been a deferral for a few simple things to be done with a resubmission the next year. I wondered when these rejections took place so have listed them below.
The majority of the information has come from the country section of this Web site with some from old WHC papers. But I can't find which sites were proposed but not inscribed for Lesotho and Fiji - could Assif identify them?
Also I couldn't find reference in the WHC papers to some of the "events" recorded on this web site
Lesotho - ????
Myanmar - Pagan. Back in 1997 the Bureau reported "unquestionable universal significance BUT problems with buffer zone, Golf course etc"
Micronesia - Yapese sites -2010 deferred (But I can't find ANY reference to this in the 2010 papers)
Qatar - Al-zubarah 2012 Referred (ICOMOS wanted deferral) "Further develop its understanding of how the fabric of Al Zubarah and its desert hinterland were an exceptional testimony", Buffer zones, Management plans etc
Jamaica - Port Royal 1988 rejected, 2010 and 2011 Blue and John Crow Mountains deferred (I can't find any reference to the 2010 deferral). In 2011 for a range of factors - boundaries, comparative analysis, justification etc.
Guyana - Kaieteur 2001 requested not to be examined as IUCN was opposed
Fiji - ?????

This indeed is an error: it was proposed for 2010, but the set of documents was incomplete so it was not discussed (we could have another category for that)

Both Fiji and Lesotho have been proposed for 2013. Of course they could still be inscribed. Same is also true of Guinea Bissau.

Angola may get its first WHS soon.

Ruin of M'banza Kongo

http://allafrica.com/stories/201209190260.html

I can't find a date, but 2014 seems likely.

Singapore has become the 190th State Party of the WHC.

http://whc.unesco.org/en/news/934

Other planned independence referendums are Greenland, Catalonia and Quebec.

As to current representability:

Not in Unesco:
Liechtenstein, Kosovo, Northern Cyprus, Taiwan, Western Sahara, Transnistria, Abkhazia, South Ossetia, Somaliland, Azawad, Nagorno-Karabakh.

Unesco members which didn't sign the WH convention:
Bahamas, South Sudan, Somalia, Timor Leste, Tuvalu, Nauru.

Member states with no T-list:
Sao Tome, Equatorial Guinea, Kuwait, Niue, Cook Islands, Djibouti, Liberia, Brunei, Monaco, Singapore.

Member states with T-list but no sites proposed:
Angola, Namibia, Eritrea, Swaziland, Burundi, Comoros, Maldives, Tonga, Samoa, Bhutan, Trinidad Tobago, Antigua Barbuda, Grenada, St Vincent, Sierra Leone, Rwanda.

Member states with sites proposed but none inscribed:
Lesotho, Myanmar, Micronesia, Qatar, Jamaica, Guyana, Guinea Bissau, Fiji.

Member states with only trans-national sites inscribed:
Zambia, Moldova, Guinea, Congo (Rep).

Since we now have a connection about member states with only one nomination I added it to the list of missing countries. I also added some special territories.

Not in Unesco (11):
Liechtenstein, Kosovo, Northern Cyprus, Taiwan, Western Sahara, Transnistria, Abkhazia, South Ossetia, Somaliland, Azawad, Nagorno-Karabakh.

Unesco members which didn't sign the WH convention (6):
Bahamas, South Sudan, Somalia, Timor Leste, Tuvalu, Nauru.

Member states and special territories with no T-list (15):
Sao Tome, Equatorial Guinea, Kuwait, Niue, Cook Islands, Djibouti, Liberia, Brunei, Monaco, Singapore, French Carribean, Chechnya, French Guyana, Faroe, Man.

Member states and special territories with T-list but no sites proposed (19):
Angola, Eritrea, Swaziland, Burundi, Comoros, Maldives, Tonga, Samoa, Bhutan, Trinidad Tobago, Antigua Barbuda, Grenada, St Vincent, Sierra Leone, Rwanda, British Caribbean, Uyghur AR, French Polynesia, Svalbard.

Member states and special territories with sites proposed but none inscribed (8):
Lesotho, Myanmar, Micronesia, Qatar, Jamaica, Guyana, Guinea Bissau, Fiji.

Member states and special territories with only trans-national sites inscribed not pursuing further nominations (2):
Guinea, Congo (Rep).

Member states and special territories with only trans-national sites inscribed pursuing further nominations (1):
Moldova.

Member states and special territories with only trans-national sites inscribed currently pursuing further nominations (1):
Zambia.

Member states and special territories with only one site inscribed and no tentative list (7):
Belize, Dominica (?), Kiribati (?), [San Marino], Puerto Rico, Bermuda (?), Reunion (?), New Caledonia.

Member states and special territories with only one site inscribed with a tentative list and not pursuing further nominations (20):
UAE, Palestine, Barbados, St. Kitts and Nevis, Vanuatu, Cape Verde, Solomons, Mozambique, El Salvador, Chad, Andorra, Haiti, Togo, PNG, Burkina Faso, Kyrgyzstan, Greenland, Netherland Antilles, St. Helena, Tibet.

Member states and special territories with only one site inscribed pursuing further nominations (5):
Benin, Dominican Rep., Paraguay, Tajikistan, Uruguay.

Member states and special territories with only one site inscribed currently pursuing further nominations (9):
Marshalls, Luxemburg, North Korea, Macedonia, Palau, Ghana, Botswana, Gabon, Namibia.

New progress in the representation:

New tentative lists for Singapore and Kuwait.
Fiji and Uyghur AR surely to have their first inscriptions. Lesotho and Guinea Bissau perhaps too.
UAE and Kyrgystan pursuing their second nominations.
Tajikistan and Namibia surely to have their second nominations.

@ Assif: you included Uyghur AR and Tibet in you overview, but not the other autonomous regions of China (such as Guangxi, Ningxia or Inner Mongolia), nor the special administrative regions of Hong Kong and Macau... Any reason for that?

Also, since you include the Isle of Man, you may want to add Guernsey and Jersey, which have a similar status. And of course there's other British territories that could be added...

Both Uyghur and Tibet ARs aspire independence which as far as I know other ARs don't.
Among the territories and dependencies I tried to include major ones with a viable chance to successful nominations. I guess I should then omit the Isle of Man...
On the other hand, West Papua and Bougainville could be included separately.

Updated version:

Not in Unesco (11):
Liechtenstein, Kosovo, Northern Cyprus, Taiwan, Western Sahara, Transnistria, Abkhazia, South Ossetia, Somaliland, Azawad, Nagorno-Karabakh.

Unesco members which didn't sign the WH convention (6):
Bahamas, South Sudan, Somalia, Timor Leste, Tuvalu, Nauru.

Member states and special territories with no T-list (13):
Sao Tome, Equatorial Guinea, Niue, Cook Islands, Djibouti, Liberia, Brunei, Monaco, French Carribean, Chechnya, French Guyana, Faroe, Man.

Member states and special territories with T-list but no sites proposed (22):
Angola, Eritrea, Swaziland, Burundi, Comoros, Maldives, Tonga, Samoa, Bhutan, Trinidad Tobago, Antigua Barbuda, Grenada, St Vincent, Sierra Leone, Rwanda, British Caribbean, French Polynesia, Svalbard, Singapore, Kuweit, Bougainville.

Member states and special territories with sites proposed but none inscribed (9):
Lesotho, Myanmar, Micronesia, Qatar (probably 2013), Jamaica, Guyana, Guinea Bissau, Fiji (probably 2013), Uyghur AR (probably 2013).

Member states and special territories with only trans-national sites inscribed not pursuing further nominations (2):
Guinea, Congo (Rep).

Member states and special territories with only trans-national sites inscribed pursuing further nominations (1):
Moldova.

Member states and special territories with only trans-national sites inscribed currently pursuing further nominations (1):
Zambia.

Member states and special territories with only one site inscribed and no tentative list (8):
Belize, Dominica (?), Kiribati (?), Puerto Rico, Bermuda (?), Reunion (?), New Caledonia, West Papua.

Member states and special territories with only one site inscribed with a tentative list and not pursuing further nominations (20):
Palestine, Barbados, St. Kitts and Nevis, Vanuatu, Cape Verde, Solomons, Mozambique, El Salvador, Chad, Andorra, Haiti, Togo, PNG, Burkina Faso, Greenland, Netherland Antilles, St. Helena, Tibet.

Member states and special territories with only one site inscribed pursuing further nominations (5):
Benin, Gabon, Paraguay, Dominican Rep, Uruguay.

Member states and special territories with only one site inscribed currently pursuing further nominations (11):
Marshalls, Luxemburg, North Korea (probably 2013), Macedonia, Palau, Ghana, Botswana, Namibia (probably 2013), UAE, Kyrgyzstan, Tajikistan.