I went to tough school on this one too. It is SO common - you should have seen the floors when I used to let 10 one year olds feed themselves! I don't even give chances - it's part of learning about cause and effect. They're too little to understand three strikes philosophy so they just end up getting mixed messages.
Sometimes it's hard to work out how they grow between the ages of 1 and 2, when hardly any food goes in their mouth, but they all do. Don't fret too much about it. You don't want to end up with food issues.
A plastic tablecloth under the high chair is good too. Hose it off, along with the baby!