I presently own 3 #1's, a 22-250 #1V, a 270 win #1B, and a 375 H&H Tropical. If you hand load these guns are fantastic, if you don't, well you'll have to settle for what you get. Earlier discussion re: how to accurize are on the money. I've been lucky as all have shot MOA (even the 375) without bedding, floating, or relieving anything. The 22-250 has had the trigger rebuilt by the previous owner and is a beutifull 2 1/2 lbs.
Other than that the only thing you NEED to do to ALL #1's is remove the safety and grind/file the front of it down to a sharp angle so it does not catch the shell upon ejection. Some can also benefit from having the ejection spring tightened up a bit to eject a case with authority - my 375 will chuck a spent case about 8 feet, I set it up as a grizz gun and wanted to make sure that chamber was clear ASAP.
Although I haven't done much to these guns, I have had one issue with the #1B (270); it is sensitive to pressure on the forend, the farther from the receiver the worse it is. If I place my front rest out near the swivel stud and bear down on the pistol grip I can make the SOB shoot almost a foot high at 100 yards! If I keep my hands off the forend completely and rest it just in front of the trigger guard, I have taken more than a couple of deer in the head at +-300 yards. One of these days I will fix this, probably by floating the barrel and bedding the barrel screw.
Cheers