I'm currently using FB Reader, which seems to be a decent e-reader for me. Unfortunately I can't see a way to edit on the fly, which is something I enjoyed doing when I was reading on my Windows laptop. My current book has a glaring error that is painful to see.
"We road up together in the elevator..."
Obviously, it should be rode.

[stillwaiting]

This sort of thing drives me up the wall as well. I've researched it and found no Android app that will edit epubs. Easy to do on my pc but then I have to make a note of all the errors whilst reading on my Kobo, edit the book on pc, transfer it back to Kobo then find some more ... ugh!

Epub readers do not allow editing of text within the book. But there are android apps that will allow editing, using this method:
In the android device, copy the epub to your preferred file manager (or doc handler). Rename .epub to .zip. Unzip the file. There will be a collection of xhtml files. If you are lucky, the files will be named by chapter, or similar. Open the xhtml file, locate the offending word. Correct it - being very careful not to touch any of the html tags eg <p> (unless you are familiar with html coding). Save the file, zip the collection of files and rename back to .epub. Send back to the ereader app.