I agree with RBC, DD et al, just stay alert and most likely you'll be okay. Most of them really ARE opportunistic thiefs. I may be a little more daring than others here. Fitness and sobriety may have something to do with it. I'm 6'2" 190lbs work-out and don't drink enough to ever get really drunk. I'll walk just about anywhere you'd want to go in SJ during the day. I try to stay even more alert in crowded areas like around the Central Market which is known for pickpockets.
Early evening restricts me only a little. For example, I've cut through Morazon Park in the early evening on many occassions with never a real problem, though I do stay more alert. The only semi-problem I ever had was one time I glanced back over my shoulder and saw a small group of guys get up off their stoop and start to follow me. I never walk too close to any such groups to begin with and they were probably still some 30-40 feet behind me. I turned around to look them in the eye and then continued on my way occasionally glancing back. They turned around once they knew I was on to them and returned to their stoop. Those types seem to hang out mostly on the southeast side of the Park closest to the DR.
The much ballyhooed TV's can be found on various corners not just around the park but on surrounding streets. I've walked by them after dark and they usually don't give me a second look. I'm not sure whether to be offended by their total lack of interest or relieved.
The rest of the Park is usually fairly empty in the early evening except for a few isolated strolling couples. There's a sort of folksy rule of thumb in CR which I've heard. If a Park is a "kissing park", meaning that you see couples hanging out or walking hand in hand, it is probably fairly safe for you to walk in too.
If you really want to know where I usually feel the most threatened when walking after dark in SJ, it is right outside the door of the BM. With all the beggars and street hustlers there as distractions, I'm always a little leery of someone trying to pickpocket me. When I'm out elsewhere it is much easier to maintain a safer distance. Of course as the evening gets later and the streets become totally deserted, its another story altogether. You never know who is lurking in the shadows. Be alert or better yet take a cab after midnight.
Street crime in SJ can be a problem and certainly has been getting worse in recent years, but, like Dino and Jag said, the same can be said of any large urban center anywhere in the world. Rio is much worse and, as Dino will tell you, even if you have a wingman watching your back you can get hit. I'm still really, really sorry about that, dude.