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
If you're buying it just to play with as your post suggested, you'll never notice any of the shortcomings of the Remington model 700 design. Personally I prefer other types/brands of actions such as my all time favorite-the Browning A-bolt, but you'll do just fine with a 700. How serious are you planning to "play with" it? If you get real serious, change extractor to Sako style. Just BE SURE to STAY AWAY from model 710s!!!!! And the revamped feeble attempt to fix the 710, the model 770 ain't much better.
I have two 700's,one in 270 that was built 30 years ago,one in 7 Mag that I bought 6 years ago. 270 shoots 1/2" groups and fits me like an old pair of slippers. I won't trade it for the world. The 7MM shoots cheap ammo into 3/4" holes,and the trigger is only getting better.
the 700 is a good rifle to play with but wouldnt dare to bet my life on it as dillenger described it is built as cheaply as possible and still make it go bang. in vietnan when the military wanted a sniper rifle the 700 was submitted but rejected. the military begged winchester to submit a rifle and they were too busy again the 700 was submited and rejected. finally with no other submissions they wer forced to accept the 700. after a few years most were out of commision.remember most were fired just a few shots a year.the american rifleman magazine did an article a few years ago about the vietnam 700. interesting reading. read between the lines and you will get the real story. however if you want a fair weather rifle and once a year hunting rifle it will work fine.
Ive never shot a stock 700 that wouldn't shoot sub MOA with tailored handloads.
Thats only about 2 doz. rifles in my limited experience, but none were bad, so that says something.
Have only had one problem, my 7mag rechambered to 7STW sheared off the extractor rivet twice...using tight fitting once-fired brass. Modified it to a sako extractor- problem solved--$40
The worst rifles Ive ever shot have been winchesters with a few old savages thrown in for good measure.
i probably would not go much above a 30-06 or .308 NATO in a remington 700. most of the remington 700s out of the box will shoot better than the average person is capable of shooting. if your looking for amore powerful round i would choose a stronger reciever. my .308 is a remington 700 but my .458winmag is a winchester...
I don't think you can go wrong as long as you stay in the 700 lineup, particularly BDL/CDL/XCR line which are Rem's approximate top of the line rifles. Like other have stated, I wouldn't care for te 710/etc and there have been some issues in the past with some features or lack of in the ADL. I haven't seen much bad on the SPS, but it is a loss leader in their line up so it will likely have some qa/qc inconsitencies.
Remington has a well deserved reputation for out of the box accuracy and even claimed in their advertising 20 - 30 years ago to be the most accurate out of the box US production rifle made. The action is the basis for several custom rifle makers, including some very heavy caliber selections and the design of the receiver is theoritically stronger since it lacks the extractor cutout required by the Mauser claw type extractor.
Some folks knock the lack of controlled round feed/claw extractor, but keep in mind the same basic extractor/ejector design is used on military full auto weapons and the posted pull strength/contacted surface area of the Remington extractor is greater than the equivilant Mauser type extractor. In terms of abusive handling, the exposed extractor on mauser type actions is more susceptible to physical damage since it is exposed that the design used by Remington/Browning.
I own Remington/Brownings but grew up with sporterized Enfield's. Conflicting stories on accuracy have kept me from a Kimber (plus I have misgivings about the light barrel profile), but it is another beautiful rifle on a more classic Mauser design.
In the end, it is a Chevy/Ford argument - more 'religous' and ancedotal than factual. Go with what you like/feels best for you and don't worry about it otherwise.