Political favors build buildings and such, http://galaxylegion.com/wiki/index.php/Political_Favor
but, if you were to ask a politician a favor, he "does" things for you

Why not make a mission thread where you perform tasks for political advisers in
order to gain more favors.

Make the Favors more usable (ie) buy off an alert.
Pump more Favors into your base Embassy for additional treaties based on a timer.

Most legions add pacts when they base alert, this gives them that option to have them on the alerted base timer, and keep the others on a static list

Good use some more fleshing out, but it's moving in the right direction, there defiantly needs to be more use for political favor, more than just a few crap planet structures.

Any other input for more uses of the Political Favor?

I've found a good use for them is to post in the GTC for an absolutely ridiculous price - most of time they sell.

I've got 100 in the GTC right now, bid is up to 10bln.

PF is only good for newer players(in term of progress). If I have to guess I'd say it's the rich resets buying them. But tbh, they lack high end practical applications. The only reason their price can go up is because they have a small supply.