I recently picked up my first Fender, a well used black with rosewood and red tort guard '05 MIA P at a resale shop for a good price. I got it even after seeing it needed some work and having read here on TB that in the early 2000's Fender may have had some QC issues and this particular P bass reflects that they did in fact have some pretty serious issues.
First issue, bridge was crooked. I mean crooked like I could see it with my naked eyes. Measuring only confirmed my suspicion. It was 1/4" closer on the G string side than the E string side. It was centered, just not straight. It was also mounted 1/2" too far back. The string thru holes were drilled crooked as a result as well. I had to remove it, fill the holes with some small dowel rods and glue and remount it properly. I left the string thru holes alone for now. I may fill them in later on if I ever decide to refin the body. A crooked ass bridge is not what I would have expected on an MIA. I have owned a lot of cheap basses in the past and I've never ever had an issue like this before.
Second issue, which is not a repairable issue or a QC problem but more of a design flaw and it seems to be inherent to most if not all Fenders and their clones. The 6th fret is a huge dead spot. The note there does not ring. It doesn't buzz out, it just decays very rapidly. No sustain whatsoever. Anywhere else on the neck is great, nice clear ringing tone, even the 5th and 7th frets, but that 6th is just dead. Some say adding mass to the headstock can reduce this, others say it just moves the deadspot. I don't buy snake oil, so I just deal with it.
Third and final issue, may or may not have been a factory screw up. The nut was sloppy as I've ever seen. Not just the slots, the location of it was off. It wasn't centered in the groove on the neck. It was sticking out on the E side and recessed on the G side, enough to where it was quite noticeable. I swapped it with a graphite nut. Again, that could have been done after it left the factory, there's no way to know for sure.
2005 also has the infamous S1 switch, which is a useless option on a P bass.
Having said all of that, now that I have the problems worked out of it, I love it. It's easily the best player I have ever owned. The tone is fantastic, full and fat without any mud. So don't let my experience spoil you from buying a Fender. As with any bass purchase, play before you buy if possible and examine it as closely as you can if possible.
Good luck and remember, have fun. That is why we do this right?