Twitter uses a jquery live form validation to do this.
There is a mod by the late Mr. Powless that does this, and more. It's 10 bucks.
http://www.boonex.com/unity/extensions/entry/Live_Validation_on_Join_form
It says it's for 7.0.3, but I would assume it still works for 7.0.5
Thanks for the suggestion, houstonlively. This looks like what I'm looking for. I've tested both suggestions that you've made and they both appear to have some issues. However, I have a feeling that this particular module may be easier to customize for my needs. Thanks again for the help.
In the meantime, if someone else can still figure out how to prevent a space bar from being entered, I would really appreciate it. I've seen some JavaScript that basically replaces whitespace with a backspace, but I haven't the slightest clue how to implement it with the Dolphin system.