I came as a postdoc with my own line of funding, so my perspective is going to be different than an actual employee. However, these are my gripes:
1. I was never recognized as a postdoc. My title was something like 'Affiliate Researcher'.
2. Given my non-status as a postdoc, I was not privy to benefits other postdocs or employees had, such as reduced cost membership to the gym or university health benefits.
3. Because I was not considered a postdoc, HR would not sign paperwork which would have allowed me to put my loans into deferment...the same was true of my funding source (NSF) (I went rounds and rounds for months trying to get a signature...nope). As such, I think accrued ~$10K a year in interest (why bother looking? When the initial debt is already >$100K, its just more stress than it's worth, IMHO), as I could not afford loan payments in addition to the ~$400/mo for health insurance. Thankfully, I was able to use COBRA through the university where I got my PhD for a chunk of my time there. After that, I had to start buying on the open market.
4. If there was a postdoc association, they were very low key. As such, I did not attend any 'career advancement' events (in the words of my NSF PM). Many postdoc associations offer things such as grants or other small bits of funding to offset the cost of things such as attending conferences. Given my non-status, I would not have been eligible.
