Tense English teacher

I had an English teacher in undergraduate school (for a BBA in Finance, so she taught a low-brow version of English for business majors) that was tough on tense and point of view. She took me to task for changing tenses too many times on a paper I had thought to be rather witty and insightful. 

I mean, who cares if its all the same? But she made me go back and modify every verb so they all agreed on tense. 

Now, in my story, I realize that not only am I writing in multiple tenses, but I am also switching back and forth between first-person and third-person, even for the protagonist. 

Of course, this is the crummy first draft, so I'm not supposed to worry about such niceties, right?

And, maybe it's okay to switch back and forth.

Gonna have to pay attention to this detail at some point. 

But for now, I will continue on my way.  Or, she will continue on her way. Or she already continued on her way.