How can I make AppEngine show the errors from the log console in the page that I'm trying to load, so that I can avoid going to the log every time?
In general, you can catch all Errors, including syntax errors, with a catch-all (except:) clause of a try statement. If you can employ this tactic in your code and then show the exception in, for example, an alert message (or any other way), you got what you asked for.
Also, Have a look at this question and the accepted answer. If you override handle_exception as instructed there, you can put code that modifies the response to the request in a way you'd like.