There are no borders or a drop shadow for context menus on Firefox 70 running on Mac OS X 10.9.5.

I have the same bug, since updating to Firefox 70 (and now 70.0.1), Mac OS X 10.9.5
Only contextual menus within the browser frame or window show this bug; dropdown menus from the Mac's main menubar aren't affected.

[Tracking Requested - why for this release]:

Firefox 69 did not have this issue on Mac OS X 10.9.5

Could you run mozregression[1] to see when this started happening? If you have never run mozregression before, simply run these three commands in a Terminal window:

sudo easy_install pip
sudo pip2 install -U mozregression --ignore-installed
mozregression

A number of Firefox versions will open in succession to narrow down when this started occurring. Simply type "good" or "bad" in Terminal based on whether or not a build reproduces the bug. Once finished, please post the output from the last run. It should give a last good and first bad revision as well as a link to look at the changesets in that range. Thank you!

[1] https://mozilla.github.io/mozregression/

This only affects 10.9. Versions 10.10 and above are unaffected.

This is an intentional effect from this patch: https://hg.mozilla.org/integration/autoland/rev/7711755e979e

Quoting from the commit message:

This introduces a visual regression on 10.9: context menus and panels now no
longer have a shadow. Only 10.10 and above support shadows on transparent windows
that use CoreAnimation; 10.9 is not able to obtain the shadow shape on those
types of windows.
I think this is an acceptable regression to take. We want to use CoreAnimation
for all window types because it simplifies the code (no need to handle two
paths) and because it avoids expensive mode switches if we realize too late
that a window we just opened is supposed to use CoreAnimation.

And from Matt's review:

It looks like 10.9 is currently the oldest version of OSX that we have users on (i.e, the next to be gone entirely), and currently has ~3.8% of our total OSX users. Losing shadows on context menus and popups for that small group seems totally fine to me in exchange for simplicity.