I have the same problem. Basically, it's caused by this: when you press the console button, it automatically adds the ` symbol (which is the same button you use for console), but like in normal text processing programs like Word, the symbol doesn't show immediately (so you can make letters like è, à , etc, by combining them with other letters). The only way around this, that I know of, is to open the console, then type a letter, then move the cursor to the left of the letter, and press Backspace. This will delete the invisible ` symbol, and will allow you to type normally for as long as the console is open.
There's undoubtedly a simpler solution, but I haven't bothered to look around yet. Probably something to do with the bind configurations or something.