I've rebuilt several lathes over the years along with other machinery. I'm not a professional rebuilder by any means, but have learned from many experts in my past including my dad, and consider myself very knowledgeable of issues and fixes that arises. Here's my two bits, the way I see things, for what it's worth.
The problem with tail stocks is, people do not clean and lubricate the ways it rides on. They always slide it on a dry, dirty filthy bed ways, period! No offense to anyone, but it is a fact with most. (We H-M take care of our stuff much better than this, don't we?) And over a period of time the ways of the tail stock base wear down and show indications as in Timgunner's pictures show. The "quick fix" is to shim up the tailstock as Robert has mentioned. The ideal method would be to re-scrape the tail stock base back to the ways of the lathe bed provided they are not worn. They will have some wear even if the bed is harden and ground, too. There are alignment issues you have to deal with when re-scraping the base to the bed ways, too. Once the tail stock has been raised up to the correct height plus a couple of thousandths, then you have to work on your side-to-side alignment.
Everyone has posted good thoughts, and they all are valid good points to check, too.
Ken