I've owned a 700P for several years. Had the trigger worked on, the gunsmith go over the wholething, bedding, crowning the barrel etc. My 700P is topped with Leupold M3 3.5x10 40mm LR and I love the combination. When I first got the rifle, it would put Federal Gold Medal 168gr. SMK's into about .75 MOA groups at 200 yards from the rest, even with that horrible 8lb out of the box trigger.
Since the gunsmith and load development the majority of the groups are now .50MOA when I do my part. I have tried bullets ranging in weights from 167 Scenars to 178gr. AMAX's with a variety of powder, primer and case combinations. My Rem 700P seems to prefer 178gr. AMAx's and 168gr. AMAX's, its shoots the crap out of them, always nice tight groups using Win cases, Fed210M primers and Varget 43-44grs. The 178gr. loads are some of my best loads, although 43.0gr. of Varget behind a 175gr. SMK produces outstanding results as well.
The only thing so far I have really noticed during my reloading is you need to find the sweet spot for your COL, mine is 2.84" for my handloads in my 700P, once you find a good load, play with the COL, you can further tune it!
Have had good success with moly bullets too but hate that gray crap all over so generally the moly bullets sit and I launch SMK's or AMAX's.
Out of the box, its a good rugged 1MOA rifle with a bad trigger. Once you get the trigger down to 3lbs and develop some good handloads (or shoot good Match ammo) the 700P has the potential to be a real tackdriver.
When I am in good practice and shoot regularily, I average around .5MOA groups with my 700P and match ammo combo. I am happy with that kind of performance. Some days I pull of a quarter inch group but if you practice any amount and know your way around long range shooting, a 700P will not dissapoint you due to lack of accuracy. I would bet than 90% of the 700P out there are capable of shooting groups better than the person behind the triggers ever can. PRACTICE, PRACTICE, PRACTICE!
Take a look at what most Law Enforcement units uses as their "sniping systems". 90% of them will be 700P's or based on the 700 design.