I think the question of Reese's intelligence, or lack of, depending on where you stand on this matter, is a tough one, because there seem to be mixed hints throughout the show, some which imply he's incredibly stupid, and others that imply that he may be more intelligent than we give him credit for.
I agree with what people said that when Reese puts his mind to something, he can seem quite bright, i.e. when he's thinking up some way to cause trouble - I'm thinking here of the episode "Smunday" when he adds paint to the trolley so it will add some "collateral damage to the neighbours" or something like that. I've also heard that as the series has progressed, he seems to have become quite the talented chef.
However, I do think that Reese also tends to come off as quite stupid in terms of academic achievement, and working things out for himself. One reason for this may be because of who we have to compare him too. Malcolm is a genius, Dewey is very bright, and Francis is no idiot. Lois is pretty smart; I think Hal can be a bit of an idiot at times, but I think that's more down to his vaguely immature, childlike persona.
We also have ourselves to compare to Reese. Obviously, I don't know anything about anybody here, but I would assume that most, if not all, of us most of the time get good grades in school, with maybe some of us consistently scoring excellent grades. The examples of Reese's stupidity in regards to schoolwork and the ability to work things out for himself could be enhanced in our eyes, because we have a whole array of mostly intelligent people to compare Reese with. If Reese was surrounded by a load of airheads, he might come across as the brightest of the lot.
I also think that Reese, on a subconscious level, may not even want to be seen as smart. He's seen the label that the Krelboyne kids have. As Malcolm said in the first episode, "Around here, being smart is exactly like being radioactive." This is just speculation, but maybe sometimes Reese makes himself appear less intelligent than he really is, because he is scared of anyone thinking he might actually have an average (or, in some cases, even slightly above average) talent or intellect. He could see intelligence as coming hand in glove with weirdness and being ostracised from other kids; therefore he chooses not to apply himself or advance his intellect.
Having said that, I do reiterate, that in areas where schoolwork is concerned, although Reese may be holding himself back, I still think that he hasn't got a great deal of scope and talent in those areas. I think if he really, really did some good, solid work he might be capable of getting some Cs. However, in areas such as cooking, and planning mischief, he definitely seems to be quite bright. But compared to schoolwork, I'm not sure these talents can be seen to be balanced out, so Reese seems more stupid than clever, even though he is talented at several things.
Has Reese's sporting prowess ever been explored in the series? I haven't seen much of it in the first season, but he seems to be quite strong, and he played hockey in the street with the other kids in the episode "Rollerskates." Maybe the area of sport is one of his strong points. Then that would bring to light the stereotypical "dumb jock" image that seems to be explored quite a lot, although most people who are good at sports are perfectly capable in academic subjects and are very good at those too.