For example,
許して正してください
Or does this make little sense?
Yes you can join two or more verbs using the te-form and say ください only once.
- 帰って寝てください。 Please go home and have a sleep.
- 食べて飲んで楽しんでください。 Eat, drink and have fun!
However, your example 許して正してください makes little sense to me, although it's grammatically correct. What is this sentence supposed to mean? "Please forgive and amend"?
EDIT: 許して正してください makes little sense mainly because 正す lacks an object, and 許す and 正す do not share the same object (i.e. you want to say "forgive me" and "correct my Japanese sentences"). Using the te-form implies the two verbs are performed either in succession or at the same time, as one set. "Forgive-and-correct" is not one set action. In this case it's better to split the sentence into two: "間違っても許してください。間違いがあれば直してください。"