What happens if you put a helium Balloon in a Microwave?

Last time I checked, helium, just like oxygen, is a gas, and, like all gases, volume and pressure are proportional to temperature. You heat it up, it gets bigger and more pressurised. Heat it enough, and the container it's in will explode. Put some tinfoil into the microwave, and when the balloon explodes, you'll get a spark, and your microwave will explode. Now do yourself a favour and take my word for it, because in this case, there really is no need for practical experimentation to back up the theory!!!

Nothing should happen. The microwaves will not heat the helium as they work on water molecules, so if the helium sample has negligible water vapour there's no water to heat, vaporise and expand. Same deal with the balloon rubber.

Aluminium ("tin") foil in an oxygen-filled balloon is a different matter. The aluminium absorbs the microwave energy and heats up quickly, and aluminium readily burns in air when it's hot enough and in pure oxygen it does so very quickly and so effectively that it explodes.

My bet would be that nothing at all would happen. A microwave oven works by sending microwaves in, alternating by sending them from 'left to right' and then 'right to left' many times a second.  This heats up water because it has dipoles, that get aligned with the field, one direction and then the other, and this quick oscillation causes it to heat up because the water particles are moving so quickly, rubbing against each other, etc.  In a helium balloon, this effect probably wouldn't occur.  As far as I know, at most you could orient the spin of the individual electrons (not the entire atom itself, like water), and this would be a very negligible effect.  So I'd guess that the video you saw was either rigged somehow, or was dealing with phenomena entirely, that don't readily come to mind.  I'm sure the tin foil had something to do with it!