Bit of a guess based on the hello world 16x2 LCD sample I've seen. The text is in the correct location (including the counter on the 2nd line) so you're not far off. The exclamation point and space characters are displaying correctly (char 32 + char 33), and being lower ASCII values they wont have the more significant bits in use. 'H' (what should be the first char) is character 65 so uses the 2nd most significant bit, as will all the others (excluding the previously mentioned space and !), so I am guessing that the 2nd wire has a bad connection or something along those lines.
I hope that helps.