But there should probably be one really quick step in the process between seeing an image on Wikipedia & downloading it for use. That is to take a quick look at the -image's- Wikipedia (or Wikimedia Commons) page to see if the reason Wikipedians think they can use it also sounds like it'd work in your use context.
Usually, all you need to do is click directly on the image (which is a good idea to do anyway, since it lets you download a higher-quality version of the image, and access full information for attribution or citation, if necessary) whereever it appears on Wikipedia.
The Wikipedia page for "Anatomy" provides a lot of great examples:
- The first image on the page is of this Rembrandt painting. Clicking on the painting takes us to https://en.wikipedia.org/wiki/File:The_Anatomy_Lesson.jpg - where we can see (towards the bottom) that it's in the public domain. Awesome - free for us to use.
- Further down the page there's an animated .GIF of an MRI scan of a human head. The image page says that they're using it under a Creative Commons "Attribution-ShareAlike" license and/or a GNU Free Documentation license. The former means its free for anyone to use as long as they provide attribution, and the work in which it is used is itself Creative-Commons licensed. This is probably not a barrier to use in a course context, because when you use a ShareAlike-licensed work intact in a collection with other stuff, the collection doesn't have to be CC-licensed, just the individual image. But it may provide a barrier if you want to adapt the original image in a context where you can't Creative-Commons-license the result.
- There is also a line-drawing illustration of pulmonary anatomy on the page. The image page states that it's public domain, from an old edition of Gray's Anatomy. Good to go for any use.
(Note: Wikipedians may not always be 100% correct about whether an image is in the public domain, but they are good at documentation, and good at self-correction. I'd say they're about as good a source of public domain information as any, these days. There's no perfect information.)
I've also sometimes come across cases where the image page shows that Wikipedians are actively debating whether that image is appropriately used (for example, from today's featured article) Again, a time when you may well be able to use it, but you'd want to consider the specifics.
Also worth noting, if you want to systematically search, rather than just use an image you randomly stumbled on in Wikipedia, Wikimedia Commons provides a searchable and browseable collection of media (more than just images) that includes tons of great, open or free, stuff.