Let's correct the sentences where there are mistakes:
a) I'm busier than my little sister. (Correct as is)
b) London is older than New York. ("more old" should be replaced with "older")
c) It's the sharpest pencil I have. ("most sharp" should be replaced with "sharpest")
d) Do you know the shortest way to the station? (Correct as is)
e) This exercise is more difficult than that one. (Correct as is)
f) Be more active in your lessons, please. ("activer" should be corrected to "more active")
g) She is the prettiest girl I've ever known. ("most pretty" should be replaced with "prettiest")
h) The boy is as tall as his father. ("as taller as" should be corrected to "as tall as")
i) He makes more mistakes than you do. (Correct as is)
j) Baseball is the most popular summer sport in America. ("popularest" should be replaced with "most popular")
k) Yesterday he started to feel worse. ("more bad" should be corrected to "worse")
l) He said that money was the most important to him. (Correct as is)
These corrections address grammatical errors primarily related to the comparative and superlative forms of adjectives and adverbs.