You should be involved from the very beginning. Design agencies can produce excellent graphical comps for use on a Web site, but they often produce way substandard markup, scripting, and CSS. Frequently they will just mock something up in Dreamweaver and deliver that as the "front end". Dreamweaver provides a very leaky abstraction of all front-end coding. And their hand-coding is often even worse. Frequently they'll just job it out to another subcontractor you may not even see or be able to interact with.
Also, static comps have other drawbacks. All text strings are carefully trimmed to fit in the space provided. For example, they'll show you a nice narrow column full of names: Fred Sparks, Jane Adams, Bob Blume, etc. And each line fits nicely on its own line. They won't have thought through what happens when a name like Mokomowatowa Damamgassitavoski, which will distort the column dimensions or have to be truncated, etc.
Furthermore, design agencies often specify a bunch of effects that may or may not be easy to do. Their solution? Just throw another framework at it. I actually heard a design agency say that in a meeting: "Well, X framework has that effect, so why not just add that framework?" And we were already using two other frameworks. (Full disclosure: I'm one of those people who believes in the one-framework rule. If you can't do it using jQuery w/ plugins plus vanilla Javascript — well, it's probably not worth doing.)
Don't get me wrong, I'm not against good graphical design. I practice it myself. But you have to be engaged with the agency from the beginning, and be able to interact with them freely, in order to get the best work done and not to have your project turn into a living nightmare.
And, yes, don't be afraid to point out to everyone within earshot that there are coding practices that should be followed. For example, element IDs are not meant to be used like class selectors. Be patient, but explain in very simple terms that having duplicate IDs on a page breaks Javascript code trying to address those elements.