As with the other connections, having the details right about the location and the boundaries of a WHS is crucial. But that's hard sometimes: notably the early WHS are very badly documented.

For 'Located in a Capital City' I've been rejecting:
- the 3 WHS in Delhi: they are all in OLD Delhi, and New Delhi is the capital of India.
- the White City of Tel Aviv: Jerusalem is the official Israeili capital, as far as I've researched Tel Aviv only has some capital functions

Feel free to react below if you don't agree with this. Or if you want to discuss other 'dubious' WHS in Capitals.

Tel Aviv is not the Israeli Capital and noone recognizes it as such. It used to be the Capital for a short while after the declaration of Israeli independence before it was permanently moved to West Jerusalem. After the Six Days War East Jerusalem was conquered and cohersively united with West Jerusalem. As an act of protest almost all diplomatic missions in Israel left to Tel-Aviv until the conflict over East Jerusalem is peacefully resolved. No country in the world recognizes Israel sovereignity over East Jerusalem. Notwithstanding all countries that recognize Israel recognize West Jerusalem as its Capital. The old city of Jerusalem which is the subject of UNESCO inscription is found in East Jerusalem so one can argue about the connection suggested for Jerusalem. Tel-Aviv, however, should definitely be excluded.

It states on the WHS website that the Red Fort is located in New Delhi. I have never been to India and cannot confirm this for myself but check the link:
http://whc.unesco.org/en/list/231

What I have gathered on the division between Old and New Delhi is that there is no strict geographical boundary, but that the 'New' refers to the city built by the British in the 1920's especially for capital purposes (it now houses also the Parliament)
(see for example the explanation
here). As all 3 Delhi WHS are pre-British, they must be in Old Delhi I think.