1. This is the oldest building in our city.
The article "the" was missing.
2. Your bag is more colorful than mine.
You need the object of the pronoun. Also, American English does not use a "u" in color.
3. Tom can speak German more fluently than the other students in our class.
You need the adverb form of fluent since it is describing how fluently Tom can speak.
4. Can you run faster than me?
Eliminate the word more. It is not needed since adding /-er/ to fast creates the comparative form.
5. The new math teacher doesn't seem as nice as our previous one.
Nice should be in the adjective form since it is describing the teacher not what she is doing. FYI-in American English math does not have an /s/.
6. The tea wasn't cool enough - I couldn't drink it.
The words cool and enough need to be switched.
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1. This is the best dessert I've ever eaten, it's absolutely delicious!
Since the dessert is better than all the other desserts, there are three or more things being compared. The superlative form is needed.
2. I think German is easier than Russian - I'm quite good at German but the Russian alphabet is so difficult to learn.
Since there are only two items being compared, German and Russian, the comparative form with "easier" must be used.
3. I think the older parts of 'Star Wars' are more interesting than the later ones - I really like Chewbaca and Han Solo in the old trilogy.
The word "more" is needed here since you can't add /-er/ to interesting. Also it's comparing older parts to later ones...this actually does not make sense. Later should be changed to newer...but that is not what this assignment is about.
4. People generally think that men are better drivers than women but women usually drive more carefully and cause fewer accidents.
In this sentence the driving skills of men and women are being compared so it needs "more" since /-er/ cannot be added to carefully.