Who cares about corrections made on italki?
Only the writer? people looking for a tutor? any others?
I also read other people's notebooks (in English) and the corrections they are given, because I always learn some sentences / word I might use in the future. In fact, I also read other people's questions and the answers they are given as well as opinions given by native English speakers in different discussions. I might read something new for me, see another way to say a particular thing or having a doubt answered thanks to another person's question, maybe something I would have not thought about before.
I read the corrected entries in English and French and that's why people who lie about their native language or their command of a language get on my nerves. When I see someone adding more mistakes to the original entry I can only think that these people are mean enough to sabotage other people's learning. Back to your question, I read the corrections to improve my English and French, and this allows me to notice which users are trustworthy and helpful. Greetings from Colombia!
I like to read the corrections made to Spanish entries. Reading corrections made by people who do them right is a good way to improve.
As a user who corrects entries in English, I also read other corrections and if there are errors, I try to correct them too. Just because someone is an English speaker (native or otherwise) doesn't mean that he/she is adept at grammar. And frankly, a lot of English speakers say ungrammatical things all the time, so just because certain errors are common (who vs. that, "everyone has his/her" and not "their") doesn't mean that we have to start incorporating them into our vernacular as grammatical.
I think that people who are looking for language exchange can also care about the corrections. It can show us if the person who corrects other people notebooks is helpful (as Camilo said) and if it is a good partner matterial. ;-)
BTW I think that those who receives corrections should "repay" by correcting in their native language. Seems obvious but it is not a custom here as I noticed :-(.