The Colt 1903 and 1908 series pocket guns (along with the even-smaller Baby Browning from FN) were what now seems almost incomprehensible---namely, pocket guns that were made every bit as well as their larger counterparts. Finely machined forged components, hand-fitted, and beautifully finished, these guns came out of an era of master gun makers who took a whole hell of a lot of pride in their craft. Oh, sorry, I'm supposed to be talking you out of it...
As far as the cleaning goes, it really isn't all that terribly hard to strip them down, but then again it normally isn't necessary for basic care, either. I seriously doubt you're going to be running these on any IDPA circuits, and it will probably be a very long time before you get 1,000 rounds through it. When you do have to clean it, remove the grips, pull your slide back, and blast the thing out with gun scrubber (a pressurized, fast-evaporating cleaner that will remove any deposits of carbon, powder, or dirty oil---you're removing the grips because while it will never hurt metal, the stuff can discolor some plastics, and NEVER get it on finished wood), and after about two minutes when that has evaporated, squirt some oil in there and put your grips back on. I bet I have put more rounds through tiny Colts and Brownings than all but a freakishly small percentage of the world's population because they're just fun to shoot, and challenging as hell to shoot well, but it CAN be done.
The breakage you describe is certainly something I've heard of as well. All I can tell you is that I've never experienced one, and I've probably put 5k rounds through these cute little guys. That said, if you're actually going to carry the thing, I'd either find a good gunsmith near you, or if there isn't one, send the thing into somebody like Cylinder and Slide and have the thing checked over.
One other thing to note---if you have meaty hands, you need to either make a concerted effort to hold low on the grip or wear gloves, because the slides will come right over the top of your hand and their little edges are sharp.
As to value, honestly that's very tough without looking at the thing. One person's "almost mint" is another person's "85%" and it just really gets tricky. If the grips are original, and the finish is original (they LOVED to re-nickel guns to cover up pitting back in the day) and the condition is as you describe, the value could be anywhere from $650 to well over $1000. Don't pay any attention to the figures listed in "The Blue Book of Gun Values" as it's a decent source for specific information regarding serial numbers, years of manufacture, etc. but doesn't keep up with current market prices at all. Colt in general has been climbing in value for the last fifteen years, and that doesn't seem to be appreciably slowing down.
Basically, they're neat as hell, and a whole lot of fun to shoot. Not necessarily the ideal medicine for stopping a charging rhino, but beats the hell out of your fists alone.
Edit to add: OH!!! Almost forgot, do not ever use any kind of solvent (gun scrubber is still fine) on that nickel finish. Hoppes No. 9 is a great product, but is not the friend of plating.
