This is a system agnostic question.
So there is a lot of leeway here. I don't even know if you are talking about with or without an alignment system or the accompanying alignment-restrictions. I don't know if this is class based (with accompanying class issues), or not. Evil characters exist heavily in non-alignment worlds, but they are rarely as one-dimensional. Spells such as 'Detect Alignment' and 'detect evil' make playing an evil character an exercise in frustration if played by an intelligent GM.
There are gameplay issues not defined. Are you talking about an evil character, or a possible evil group?
What level of maturity is the game being played? Setting with alignment systems tend to be a lot less realistic and a lot more balck and white. Mature settings with more ambiguity and more mature thesmes leave more room for the evil character to act in. If the world has a clearly defined good but a very large undefined population, that gives cover an anonymity.
Most religeous systems in RPGs revolve around Patron deities...whereas evil in the real world normally believes itself to be wrapped in the rightness of their religion, Most evil deities are simple-minded. Hard enough to be an evil character in town with temples to only good deities, harder still to be a cleric or priest. It requires a GM with experience and good setting design skills to create more layered, textured religions with subsets and cults that would allow for an evil priest to hide in plain sight in a populaiton center.
All of the above aside, just as 'Lawful-Stupid' is not a real alignment, 'stupid-evil' does not have to exist either. An evil character may merely act with their own long term goals as more important than everyone elses. Backstabbing is rare and cooperation makes sense most of the time...except for the rare case that is does not.
Also, by the terms of most alignment systems, anti heroes such as Elric Or the Grey MMouser would be considered evil; yet these are great characters to be able to play, and would be part of great campaigns...with the right GM.
The biggest challenge I see to playing an evil character is the GM. Running a setting or campaign that is open and realized enough to allow for a non-good, selfishly motivated PC or an anti-hero requires a more talented GM than a normal, vanilla, heroic game.