i think they would cause problem cuz you mask your link. And this case, they cant track where is your traffic from and they could ban you if you use adsense.
Thats stupid. They are not going to ban your adsense account just because you use a link shortener as a traffic source. If that was the case everyone who promotes their website through twitter would be banned.
It won't cause any problem with google. People use them all the time especially on Twitter where every character counts.
as long as u position the link at a good spot for them to see and click it doesn't matter but i have heard from some people specially web novices that they don't click the tinyurl because its looks unreal and maybe it gives them a virus or something
if its affiliatlink than it`s ok. but if its link to your site via tinyurl you will not gg any value for this