My recent visa experiences follow.
I turned 60 last year which, at least in some provinces, creates problems with residence permits. In particular, Fujian is reportedly reluctant to issue them for older folk. I've been told this is policy brought down from Beijing, just not enforced everywhere. I've also been told that there is no age limit in policy, it's just that employers are required by SAFEA to provide medical insurance for all employees and do not want to pay the higher premiums for older staff. No idea if either tale is true.
I had an offer from Hua Qiao University, Quanzhou, Fujian. Then email saying me being 60 was a problem, but nothing they couldn't deal with. Then withdrawal of offer with the explanation that the PSB had already made exceptions for two of their returning staff over 60, was not willing to do it for a new hire.
So I got back to former employer Yang En, in the same region. They say it is not a problem, and the limit is 65 anyway. Should see in a week or so if they actually produce a visa.
In 2006, I moved from Zhuhai to Yang En and had a tourist visa when I arrived. They said they could not get a residence permit from that; I had to go to Hong Kong and re-enter on a Z visa. No problem; I actually went to Macau (much easier) and they paid for the trip.
This time, I'm on the last days of my Nanjing residence permit. No trip to HK/Macau needed, but both Hua Qiao and Yang En asked for a release letter from the previous employer, said this was a gov't requirement for residence permit. OK for me, but might
be a real problem for someone leaving a screwed-up job under tense circumstances. If old employer can hold that over your head, they have a lot of leverage.