I guess I really got lucky after watching the video Glenn had about trailer tires. I replaced my trailer tires last year. The ones I got rid of were only 17 years old. The replacement tires are slightly shorter than the original factory tires. I still have the original spare that matched my old tires. My question is If I had a flat and had to use the spare will it present any problems towing with two different size tires on it?  This is a single axle trailer. Thanks for any info.

Not ideal but short term your spare would be ok just don't leave it on permanently.

. 

They are independent of each other and should not effect anything but ride height. 

A spare tire is just that. No different than a donut spare for the car. You put it on temporarily until you get the regular tire fixed/replaced