need a few sentences checked

1) He wears this kind of shirt.
2) He ate like there would be no tommorow.
3) I am uncertain as to Tim's opinion on this.
4) The students should turn in one paper per week.
5) Eventually, mankind might destroy the world.

We are supposed to check these sentences and check to see if there was any rules saying that they were incorrect and Im down to these last few and I can prove them wrong but some of them just dont sound right .....

thanks for the help