The Honda Fit uses a timing chain instead of a timing belt (I believe all Hondas switched to timing chains around 2006).
According to
CarComplaints.com, there aren't really any major things to look out for. Honestly from what I found when researching this as a possible vehicle very few complaints were out there. I did find a couple related to power steering failure.
Can't really help with the rusting part since I don't own one; obviously check key areas such as the license plate bolts, wheel wells, fuel tank cap, hood, underbody, etc. A brief Google search didn't seem yield any abnormal results.