After replacing a transom due to improper sealing of through hull steering fittings I am interested in contracting for a marine survey when looking at another boat. Does a survey include checking for moisture content or damage,and if they do how do they check it?

They use a moisture meter and any good surveyor should test for moisture as part of the standard survey.

Are they able to do this through the glass or do they need to drill holes?

they run a moisture meter all over the hull.no drilling of holes as far as i know.just had one done.those guys know where to look for water.

The old timer surveys used a rubber mallet to pound on the hull and detect moisture, guess the wet spots sounded differently. Today they use moisture meters.
I've heard horror stories about bad surveys using either method.

There are situations where the surveyor must use some flexibility in the method he uses to detect flaws, repairs or water intrusion into the hull or related structures. NEVER is a surveyor allowed to do a distructive operation to a vessel. The moisture meter must be the non-invasive type. A boat with bottom paint gets treated differently than a gelcoat bottom. If the boat with bottom paint has been out of the water for a minimum of 48 hours, then a different procedure is required.

I find a rubber mallet to be inferior to a phenolic or steel hammer in determining the soundness of the vessel when sounding the hull.