It is never a good idea to suddenly switch your dog's food, even if it is back to something he once ate. That is bound to cause diarrhea. Just because he was off of his food for one day, especially after being so sick the previous day, doesn't mean that what you are feeding needs to be changed.
The dog's coat could be dry simply due to the time of year. If you think his food is not of high enough quality and has too many by-products in it, as well as too many (not whole) grains, investigate the labels on other feed. If you decide to try yet another feed, you need to wean him off the one to which he is accustomed and slowly introduce the new food by mixing it with the old. The first ingredient listed on any quality dog food should be meat (or protein) and not a "meat meal" or "by product".
Personally I wouldn't be so quick to switch unless the quality you are feeding him is not good. I am not familiar with the brand you mentioned. My dogs eat "Wellness Super 5 Mix - Senior Light". If they are fed anything different, they will both have very loose stool. Your dog probably had an upset tummy from the day before and was naturally fasting. Dogs don't always have to eat every day. I would only worry if it went on for a couple of days and if he weren't drinking enough fluid.
There is a website that many of us have used, but it might be a bit outdated by now. It will give you an idea of how food is rated though, along with what is considered optimal ingredients. It is http://www.dogfoodanalysis.com