I think mdf core plywood is really for cabinet work and not practical or intended for most scroll or fret work projects. And any plywood: mdf core, veneer core, classic core or baltic birch will have some finishing issues on the edge. Here's a practical application of mdf core plywood (see pics). The drawer fronts along with the rails and stiles are solid wood. The door panels are 1/4" mdf core plywood. I built these about 6 years ago. I think the finish of the solid and plywood are identical. And if you consider the cost and time in building the entire door from solid wood, I'd still be planing and gluing up wood.
I think (and I'm pretty sure others agree) poplar is a pretty good choice for scrolling. Readily available, reasonably priced, cuts well, accepts paint or stain (with some effort) and glues well. And while oak had gotten attention in this thread I'll add my 2¢. I've used red oak on several projects and what I like least is the open grain. To get a really nice finish you must use some kind of grain filler. Years ago I used Watco and wet sanded to fill the surface grain. Now my process is to use Timbermate. Doesn't matter it's always an extra step.