There are tweet ads, yes. They are usually marked as "promoted"
I found it useful to "report as spam" the account they were coming from so at least you only see them once...
I found the new layout to be headache inducing for my english-speaking, left-to right-reading brain so I switched to the Chrome plug-in Silverbird on TVGugs recommendation... and haven't seen the promoted tweets since. Maybe that's because I'm using lists more... but it solved a lot of problems for me.
I have a lovely PC. It's all fast and wonderful. It plays games such as F.E.A.R, Black and White 2 and The Movies perfectly well, and does every non-games-related task I wish to throw at it without breaking a sweat. Well, except for one thing.