My doxie threw up twice yesterday and sometime in the middle of the night went into the kitchen and left me a large amount of diarrhea to clean up this morning. He is acting fine so should I be concerned? What really is a good sign for taking him to the vet?

Honestly that is a great sign he needs to get to the vet. How old is he?

He is a little over a year I think. He is playful and active still so I wasn't sure if it was just something working through his system.

Ok that's good. I immediately think parvo when I hear of a dog vomiting or with diarrhea. But being that he's a year old or so, that's likely not the case. I wouldn't rule it completely out, it's just not likely. Has he gotten into anything that you know of? Tuscany's doxi got into some apple peels not to long ago and had some issues. https://www.askmehelpdesk.com/dogs/tuscany-sick-129079.html

A quick phone call to your vet at least and see what they have to say. Certainly keep an eye on him though. Dogs can dehydrate quickly when they vomit or have diarrhea.

I must admit little experience with Doxies, but what I read here suggests they are as bad as Labs about foraging indigestables. Often their body works at expelling it at both ends. If that works, they are back to normal soon without medical treatments. I wouldn't go running to the vet right away. I would take care the problem doesn't become worse over the weekend. Diarrhea plus lethargy does mean immediate attention.