I successfully completed my Master's dissertation a while back and I've decided I would like to publish it online to help others and probably print a copy for myself to up on the bookshelf. The dissertation was good but it wasn't perfect. Other than the usual typos, there were a few minor mistakes with how I presented the data which my professor pointed out. Should I correct these things before publishing or is that not the done thing?
You should always correct and polish your work before publishing it. Therefore I would suggest you implement the fixes recommended by your professor, and correct the typos you mentioned. Having done this, you should point out somewhere in the publication that this work was partially adapted from the document you submitted to your institution, stating that you fixed a couple minor things.
As @darijgrinberg suggests here, you should also remove any official logos and statements that might be included in the document, as to avoid it being confused with an official university publication, let alone copyright breaches.