The game system can seem comewhat cumbersome at first, as most combat actions require the rolling of lots of d6, but it took only a session or two for my groups to get used to the game mechanics. By contrast, the richly developed background (backed up by dozens of sourcebooks) seems to come easily to most players; the events of the world's "future history" stick in players' minds.
Shadowrun 2nd Edition is quite an improvement over first edition; while design and production values have been high in both editions, a number of rules problems have been cleared up and/or streamlined. FASA impressed me with their dedication to the customer by putting 2nd edition conversions of all of their 1st edition source material in the 2nd edition rulebook. You won't see much of this out of TSR or White Wolf. The biggest problem with Shadowrun, much as with many other cyberpunk RPGs, is the Matrix.
There is little that a gamemaster can do about the Matrix. It is a place where only the decker among the runners can go, and while he or she may be heavily involved in what is going on in the Matrix, the rest of the players quickly acquire the bored stare that gamemasters dread. The best suggestion that I have is to restrict the long-version Matrix runs to times when the rest of the PCs are on break or schedule them simultaneously with combats. That way the GM can run one round of combat, one round of Matrix, and so forth. This also heightens the tension for all involved.
With the recent passing of Nigel Findley, author of about a dozen Shadowrun sourcebooks, I worry that the overall quality of the game product will decrease. Carl Sargent, co-author of some real clunker sourcebooks (Tir na NoG and London come strongly to mind) is the line developer now that Tom Dowd has made his way into FASA's lucrative computer-game division, and that worries me too.
A trend of "magicking up" the game has also been happening since the early adventures. The first two that I remember were mostly non-magical, and dealt well with technology-based issues, but with Harlequin, Bug City, and Harlequin's Back coming out recently, and a number of mostly-magical adventures having been previously published, I worry that SR is shifting from an even balance of magic and high-tech to a magical world which has cyberware. And that isn't why I play the game.
We were in on the FASA Shadowrun Open at Gen Con three years ago, and again last year. We came in second place two years ago (I happened to run a decker named 'Generic'); I was disappointed to be unable to get into the open this past year. It filled up very quickly, apparently. Mike Colton runs the Shadowrun and Earthdawn tournaments for them every year, and they keep improving.