What would the purpose be of having a vertical cleat on the side? A decent width horizontal cleat, installed plumb, will fully support the mirror without any movement. Are you worried about it somehow moving sideways or swinging out from the bottom?

If I use one of these at the top, http://www.homedepot.com/catalog/productImages/400/ce/ce640ed5-ee60-4ac3-b0c2-0e16649bca25_400.jpg (supports 60 lb. max) which is ~7.5 inches across, what would I need to ensure that it is level vertically?

This post was edited by argh on Fri, Jun 13, 14 at 18:39

If you use a decent level to make sure the cleat is mounted on the wall horizontally plumb and you mount the second part of the cleat on the back of the mirror so that it is parallel to the top edge of the mirror, then it will be plumb vertically.

You're over-complicating this. Just be accurate in installing the cleat. If you install it and it is a wee bit off you can just build up one edge of the cleat on the wall with a little masking tape to elevate the low side. Trying to use two cleats is asking for trouble.

Also, how do you intend to mount a cleat to the back of the mirror given that it is frameless? Is there something on the back you can put screws into without damaging the mirror?

No insult intended, but it sounds like you don't have much experience with hanging things like this, and I'm guessing that you don't have an accurate level. If so, buy one...a decent one for your purposes is under $10.

Here is a link that might be useful: Torpedo levels

What I plan to do is make the mirror float slightly. Then, by magic (mirror adhesive), a small piece of 3/4" plywood would be adhered to the back of the mirror with the cleat screwed to that. Does this make sense?

That makes sense. However, You probably want to mount a second small piece of plywood to the bottom of the mirror or else the bottom will tip in and touch the wall.