Quite a few in my opinion, but a lot of guys on here love them.
On the Positive Side: They are very common, probably the most commonly produced action, and thus, the most widely designed for action in the market place. Lots of good quality drop in parts ( like stocks, triggers, safeties, etc ). The Remington is by far the easiest of actions to work on, the metal is soft and isn't hard on tooling like the Model 70.
On the Negative Side: The walls of the action are one of the thinnest on the market, and since the action is the anchor for the barrel, thinner doesn't necessarily equal better. The action is going to be asked to support your barrel's weight, and also counter the torque generated by the bullet as it enters the rifling. The thicker your action, the better for overall accuracy, because it will be a more stable anchor for the barrel. The extractor is one of the worst designs out there, so much so that the Army has refused to entertain the standard Model 700 for their new custom built Sniper Program in .338 Lapua. Generally custom builds include replacing it with a Sako style that is more reliable. The bolt handle is another weak spot, as it is a three piece, braized together contraption instead of a more solid one piece unit.
All in all, it's a decent action, and if you get a good price on it, it's an easy gun to tinker with because of the vast aftermarket that is available. It's not my top choice for building a true tack driver, but it can be made to shoot extremely well with a little bit of love. YMMV.
I actually did a write up for the website comparing three popular actions if you wish to read it in detail. Rifle Action Comparison