I pretty much exclusively do group roleplays, and I look for four things in interest checks in exactly the following order.
First is decent formatting. If your interest check thread looks like it is the embodiment of a schizophrenic rainbow or makes me want to gouge my eyes out for any other reason, I'm not going to bother reading through the thing. I've lost count of the number of times I've opened an interest check, cringed at the painfully terrible formatting, and closed it without giving it a chance.
Second thing is basic skill with the English language. It doesn't have to be perfect, but if you write so poorly that it makes my inner grammar Nazi froth at the mouth then I'll just save myself the annoyance and not join. That may be somewhat elitist, but I make no apologies for it, it's just how I roll.
If my interest is not immediately killed by formatting or grammar issues, the next thing to look for is to see whether or not the general idea actually sounds good to me. The premise has to be something that makes me say "yeah, that'd make an interesting story." To do that, first off there has to be a premise, something that actually hints at there being a real foundation for a plot. As fun as it may sound, "sandbox roleplay" translates into "directionless mess that will die quickly" 99/100 times. Also, ancient premises like "let's play a band of heroes off to get the world-saving MacGuffin" need something more to make them interesting to me. It's just a super subjective test of general interest after getting past possible presentation problems.
Finally, even if the general idea interests me, there has to be something in there that makes me think "awesome, I wanna make a character for this right now!" This largely comes down to the setting information, and as such I'm often willing to express tentative interest for something that meets the above three criteria and wait to pass final judgment after reading whatever they present for the OOC. It doesn't matter how interesting the premise is to me if there's nothing specifically about that roleplay that inspires me. After long experience of repeatedly getting burnt out on roleplaying after pushing myself to pursue interesting premises without that spark of inspiration, I've found it just isn't worth the time or effort to bother with them any more. This may sound extraordinarily picky, but it's really not, I find things that inspire me to make characters in the vast majority of roleplays with interesting premises. It tends to be mainly roleplays that end up having generic settings or sandbox roleplays that fail to do this.