1. My understanding is a sentence like A is B is C, unlike A is A is A, isn't acceptable. If you say yah, there's no argument whatsoever. If you do nah, let's see the following.
2. The whole sentence is
Brush your teeth first, because the two things I can think of that are worse than a bad style are bad breath and bad manners!
The part in question is
the two things I can think of that are worse than a bad style are bad breath and bad manners!
3. Let's let
A = the two things
B = I can think of
C = worse than a bad style
D = bad breath and bad manners!
4. To put it simply at first, let's get rid of B temporarily.
5. If the pattern is A that is C is D or A, which is C, is D, it becomes
the two things that are worse than a bad style are bad breath and bad manners!
or
the two things, which are worse than a bad style, are bad breath and bad manners!
6. If the pattern is A is C that/which is D or A is C, which is D, it becomes
the two things are worse than a bad style that/which are bad breath and bad manners!
or
the two things are worse than a bad style, which are bad breath and bad manners!
7. If the pattern is A is C and D, it becomes
the two things are worse than a bad style and (are) bad breath and bad manners!
8. Now, let's add B to the above sentence and see what we can get.
9. If the pattern is A that B and is C is D or A, which B and is C, is D, it becomes
the two things that I can think of and are worse than a bad style are bad breath and bad manners!
or
the two things, which I can think of and are worse than a bad style, are bad breath and bad manners!
10. If the pattern is A B is C that/which is D or A B is C, which is D, it becomes
the two things (that) I can think of are worse than a bad style that/which are bad breath and bad manners!
or
the two things (that) I can think of are worse than a bad style, which are bad breath and bad manners!
11. If the pattern is A B is C and D, it becomes
the two things (that) I can think of are worse than a bad style and (are) bad breath and bad manners!
12. To be advised, if any.