I think scores are a good way to add a little competition while still maintaining a spirit of collaboration. It doesn't directly affect the game (you can't see it unless you open the menu), it doesn't punish the players XP points or credits wise, since everything is evently distributed at the end, and it brings a sense of satisfaction with every accomplishment.
That said, even though the system accounts for all types of activities (from kills and assists to revives and grabs) it is at its heart uneven in the way it is related to the existing classes. While heavy damage dealers (like infiltrators and biotic exploders) might find great joy topping the scoreboard and competing with their peers, support classes are often left behind, as useful--if not vital--as they are for the team.
Is it a bad thing? Personally, I don't think so. My favourite classes are the Infiltrator (very offensive) and the Enginner (mostly defensive), and I keep very distinctive expectations for my performance with each of them. When playing an Inf, I try my best to kill fast and get points (never in detriment of revivals and objectives, of course). When playing an Eng, I relax and focus on deploying my decoy or healing my squadmates, for I know I can't directly compete score-wise with a heavy damage dealer (although it has happened on occasion). Provided the players are aware of their role in the battlefield and don't try to be the best at everything, the match should procede properly. In short, it's all about common sense.
It would be nice if support classes had more opportunity to shine. For example, giving points for each revive (in addition to the badges), or each time an enemy attack/destroy a drone, or as a bonus for each sabotaged synthetic. However, I'm afraid that would be awfully complex to implement. Plus, it stumbles on the very fact that each class plays differently and thus their progress cannot necessarily be compared in an homogeneous fashion--i.e. actions that make the soldier great are not the same that make a great adept and so on. Which is, you could argue, the very conceptual flaw in the scoreboard system: it judges very different things using the same criteria.
I think I said too much, though. I'll let the discussion proceed.