The tile under the toilet are a little uneven. Once I tightened the screws the toilet stopped moving but I am worried there may strain on the china. It does not rock at all but I can see a little gap in the front off the floor. About an 1/16 of an inch, very small. Has anyone encountered this and do you have any recommendations? Is this an issue or should I just forget about it.

The plumbing experts will be on later but I really don't see an issue here. If the toilet doesn't rock and its only 1/16 gap I wouldn't be concerned. If the gap bothers you. You can caulk around the base of the toilet. I have run into this problem a couple of times and haven't had any problems. GOOD LUCK, AC

Take the bowl in both hands. Rock it from side to side. Now see if it will rock front to back. If it won't move then you've done a good job.
Now take a tube of Dap White Tub and Tile Caulk and caulk the base of the bowl to hide the crack and give your job a professional look. Good luck, Tom

No rock. I will caulk and be done with it. Thanks!

Tom and ac101 are very much on the money, no rocking no problem. It is common for tile floors to not be perfectly flat especially if they have been redone by a DIYer

I take that personally! Just kidding.