My current P1 is one of the most accurate pistols I have. It is capable of chewing out the same hole at 15 yards and past that is more accurate than I am capable of shooting.
There are a lot of P1s on the market right now. My advice, use patients and look at what is out there. There are some upgrades that make them more desirable - but are not necessarily deal breakers. There are thousands in existence without them that are still going strong.
Upgrade 1 to look for is the Hex Bolt. This upgrade was added to give the locking bolt a steel surface to ride on. It decreases wear on the frame. Most Walther(s) would never be shot enough for this to be a problem - but it is a nice feature. It is a hex bolt easily seen on the frame.
Upgrade 2 is the fat slide. The older P38s/P1 did have a small issue with slides cracking. probably from using ammo that was out of the design specs. The fat slide is easy to recognize from the serrations that extend forward of the safety.
Upgrades 1 and 2 see pic
The P1 is a great classic pistol that used properly will outlast most shooters and become a family heirloom. One thing on the P1 is the ammo used in them. These guns were designed around the 115-124 grain standard velocity 9mm ammo. Hot rounds (+P) or heavy grain bullets are not recommended.
The alloy post-war frames are not necessarily a bad thing. I've been shooting them since the 70s with no problems. Most of the P38/P1 history has been built around this frame and it was a European service pistol in this configuration for over half a century. The war time steel frame guns bring a higher collector price, but they have their issues too - war time QC was not always its best. Like any product - it was upgraded and tweaked as it stayed in production.
One additional comment on the P38/P1, sight adjustment is with the front sight only. If you try and drift the rear sight it will damage the top cover on the slide.
For more info on the P1/P38 go to these forums:
http://www.waltherforums.com/forum/
http://www.p38forum.com/