This is a great question!
Here are some of the common mix problems I run into:
Bass response is off, either too much low end, or not enough. As many of you know, bass response in the studio/monitoring environment tends to be the hardest thing to get just right. So, many mixers may be working in environments that are not giving them a true picture of the low end. That translates to low end issues in the mix. Of course many of these can be remedied with EQ.
Over compression. This one is difficult, as you can not uncompress the mix. As I mentioned in a previous post, I usually do my best not to make the issue worse, and maybe use a few tricks to regain transients and a sense of dynamics.
Vocal level vs rest of the mix. This is one of the most difficult to deal with. What I mean here is a mix where the vocals are really loud (and often really bright) in comparison to the band. Almost anything you do in mastering will make the vocal worse, and there is very little you can do to make the band better. I usually try to push the vocal back in the mix with stereo width enhancement, but this may make the kick and snare and other center tracks lower as well. This is the kind of major problem that can be cured with stems. All that's really needed in this case is an INST stem and Vocal stem. Of course, this kind of mastering job will take a bit longer than the norm.
You're last question was about sending mixes back for tweaks. This can be a bit of a minefield. Some mixers are very receptive to feedback and making adjustments, and some are not. Also, because mastering is the final creative step of what is often a processed pushed right up against a deadline, in a lot of cases tweaks may not even be an option. In a perfect case scenario I will have a good open line of communication with the client and the mixer, and can send mixes back for tweaks. A lot of issues have to come together just right for this to happen!
You're last question was about mix tweaks