High-powered characters are fine if they're in a situation where they won't spoil the fun for everyone else. For example, if everyone in the story has superpowers, giving your character similar superpowers is probably not cause for alarm. Or if you're writing a big project about a Twine Wars, there will be major, powerful characters rising to prominence amid the dramatic political changes.
However, in some situations it can unbalance the story and give one writer or character all the limelight. If there is a disparate group of humanoids working together to solve a problem, and a dragon with a big sword comes and works out the puzzle in two seconds with her enormous intellect, heals everyone's wounds, kills all the bad guys and rescues the prince's dog, all in one massively long post, this is not good cooperative writing.
This depends largely on the situation. If the dragon is faced off against equally powerful characters, that may be fine and good. Alternatively, she may be able to interact well with all those less powerful characters if the situation of the storyboard is such that she can't solve everyone's problems instantly.
(But writing her into a story purely on the promise that she won't decide to use her abilities should probably be avoided. Why use that character at all in that situation? Why not choose someone who would better suit the board?)
Strange as it may seem, this "too powerful is unbalancing" principle has an inverse. If you're writing a weak, helpless character among capable characters, it can - but this does depend entirely on the situation - be just as annoying.
Carbon copies are boring. A range of abilities and capabilities is a good and realistic thing to aim for. There's only a problem if one or more writers isn't/aren't having fun. And if you're getting the limelight, step back next time and let another character take their turn.
Also called 'puppeteering' or similar terms, this type of godmoding involves writing someone's character for them. If you put words into someone's mouth or make them react without their writer's permission, that's generally not good.
In some cases it can also include writing the character doing nothing (or assuming they will) - if, for example, you threw a snowball at them and didn't give them a chance to duck, or carried on a big long conversation in front of them without giving them a chance to interrupt.
In all these cases, discussion and agreement with other authors is the key: "No, keep 'em talking: Nico and Johan Stuck are just going to listen." / "He's facing her and he's got pretty sharp reflexes, so I'm going to say he'd dodge it. Anyone behind him it could hit instead?" ([ahem])
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