Faulty digitisers (the glass panel and membrane over the screen which turns touch input into OS interaction) does cause random or specific issues with interactions appearing to happen on their own.
You can either send it to HTC for repair like Lekky says, or if no warranty available, buy a desire digitiser and get a mobile phone repair specialist to fit it.
My Fiance had this on her Hero (although different symptoms) and it now works perfectly.