If it's not Honda glass it will not say "Honda" on the windshield (in small letters on one of the corners). I had the windshield replaced on mine after I picked up two big rock chips right where I look at while driving. Glass-pro replaced it with a Pikington brand windshield and there were no issues with it. Often times there will be discount glass installers who will use second grade glass which aren't perfect. The installer could have not put down enough of the windshield cement too if your getting leaking.
Is the windshield ok, or are there optical imperfections like waving in it? I've also seen bubbles in second grade glass before. If the windshield doesn't look like a second grade one then your probably best off having a glass installer look at it and see how much it would be to pull it out and reinstall it properly. If the glass is a blemished second grade one then it might never be quite right and you may want to consider having another installed. Honda glass is very expensive. My Civic Hybrid needed a windshield and they put a PPG brand glass in it and it has been great.