- The top/most effective contributors are given visibility
- It gives community members a goal to aspire to
- There are areas where such reputation may be used as an incentive (if a user helps moderate a post, give them +2 reputation, for example)
- The reputation system may become biased towards more active/vocal participants
- A negative reputation may indicate something more severe about the user than is actually the case (a big red -200 score on a profile sets other users' alarm bells ringing)
- Members can become victims of revenge attacks by people repeatedly downvoting others, should the system work based on other user input rather than statistics
To determine whether a formal system is the correct choice, one may wish to evaluate how they want users to be analysed in terms of their performance. Activity? Quality of communication? Popular opinion? The answer varies for every community and their owners. If you wish to explicitly make posting lots and to a high standard a focal point of your community then a reputation system is a good way to add an extra touch to it.
However, as aforementioned, people can fall foul to the system if it is incorrectly configured.
Edited to include revised question:
Statistically, a formal reputation system is doing more harm than good when you have extremes for your members. Some will have super-negative scores, others really high. If many people (think normal distribution) have a low score (i.e 0) then something is afoot. This is either a clique forming where people upvote their group and downvote everyone else, or can actually be from the more vocal users essentially blotting out the rest (by gaining so many more points just because they're active).
In addition to this, people are often more inclined to upvote more reputable members and downvote those in disrepute, simply because of the snowball effect.
From an opinionated perspective, you can see when a system is harming your community when people make threats or references to their reputation. If someone is saying "I'll downvote you for " or "Well, I have a reputation of <123>" then this can cause friction between members. Ultimately, there should be a sense of the mood within your community, judged by their use of language (being terse, sniping at each other etc) and if you feel this is rapidly becoming a hostile environment then you may wish to consider suspending your reputation system plugin, as it may be to the detriment of your community.