Mine too! My daughter is FINALLY getting her first tooth and she is 15.5 months! Just like yours, she likes all foods, especially finger foods - it just takes a looooong time at the table sometimes.
She is developing normally or even above average in almost every other way. I have been told that when teething occurs later that language development can, too (which I guess makes sense because we use our teeth to pronounce so many words), but her pediatrician seems to think she is on par with this, too.
And like you, we thought she was teething many times before - even her daycare asked me to bring in some orajel when she was about five months old because they were convinced she was teething! - and they see it all the time, so you think they would know...
I do worry about her nutrition because she tires of the mushed food and likes to feed herself (finger foods usually, working on the spoon!) and it takes her sooo long that I wonder if she is just tiring of being strapped still in a high chair or is actually full. So, I still breastfeed her before bedtime and give her a multivitamin and an occasional pediasure (or similar brand), so I hope I am filling in the gaps.
I am commiserating more than giving you any advice, so let me think of something - two products I have found useful for my late-bloomer are those "safe feeders" (like a little cheesecloth bag that attaches to a handle, so you can put apple slices or similar inside them and they can knaw on them and get the juice, etc without the normal choking hazard) and I found that that Baby Bjorn makes a bib that is hard plastic that scoops out like a wearable bowl (there are other brands out there, too) and it catches all the debris my duaghter has trouble keeping in her mouth as she "gums" her eggs, or peas, etc. She'll even reach in and grab the food back out of the bib and try again, so it's less frustrating for both of us! Her with feeling independant, me with less mess!
Take care! I will look back and see what other people write because I almost asked this question myself several times!!!