The positives of Strava have to do with the product itself while the negatives are mostly due to the people using it.

Pros:
1. Your friends are on it. Being social is good.
2. Segments are fun.
3. It's as accurate as anything else out there.
4. The app and website are very stable and mature at this point.
5. Flybys are a bit creepy but interesting.

Cons:
1. Accuracy varies by device causing ego fails. I've had people I'm riding with post an avg. up to 1 mph faster than me over a relatively short ride even though they're sitting on the wheel and I'm taking pulls (swear to God). I got a new phone and suddenly my AVG dropped by at least 0.5mph over courses I ride all the time. Also, comparing it to a wheel mounted computer shows that Strava's avg is a bit wild.
2. You get to a segment, you're pulling, someone on your wheel pulls around you at the last moment and claims the KOM. Or you get to a segment, someone riding a draft bridges up to you and gets the KOM. Happens all he time and results in more ego fails.
3. Stupid cyclists defining segments that have lights, dangerous downhills or other obstructions. This encourages dangerous riding. Also, people not being careful with the start and end point of segments (e.g. putting the end point right at the light rather than 50 yards prior to the light and giving people to slow down) causing the same issue.
4. No accounting for riding with a group, headwinds or surface conditions (e.g. you might be riding on gravel) make the power estimates and ride-to-ride comparisons difficult. Also, every single KOM in my area was almost certainly set with a group riding in a strong tailwind.