Adding RB Label as this is a recent Regression. Please remove if not required.
Thank You.

<paper-menu>/<iron-overlay> or whatever this is should probably be hiding its overflow while showing

Re #2:

<iron-dropdown> does try to hide overlay while animating. The problem is that it doesn't reliably cancel any current animations when starting a new one. As a result, starting/cancelling animations in rapid succession causes the element to get confused about whether or not it is animating.

On top of that, since the animations change the height/width of the dropdown, it's possible to cause some wacky glitches to happen based off the height/width being incorrect when the menu is opened.

<iron-dropdown> cancels the previous animation synchronously when `opened` changes [1], and plays the new animation asynchronously [2]

[1] https://chromium.googlesource.com/chromium/src/+/master/third_party/polymer/v1_0/components-chromium/iron-dropdown/iron-dropdown-extracted.js#138
[2] https://chromium.googlesource.com/chromium/src/+/master/third_party/polymer/v1_0/components-chromium/iron-dropdown/iron-dropdown-extracted.js#159

I'm still seeing some interleaving of the two animations, though. I'm not 100% sure why.

Instrumenting neon-animation-runner-behavior to log when animations start and end, I see:

neon-animation-runner-behavior-extracted.js:72 start animation: close
neon-animation-runner-behavior-extracted.js:72 start animation: open
neon-animation-runner-behavior-extracted.js:91 finish animation: close
neon-animation-runner-behavior-extracted.js:91 finish animation: open

The easist way to reproduce this on chrome://history is:

1. Click menu button, wait for animation to finish
2. Move mouse to hover over a different menu button
3. Press escape
3. During close animation, click menu button

Retested the above issue on Windows-10 machine using Canary chrome version 54.0.2822.0 (Official Build). It's still reproducible.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/e022b8b94971d07b93ed758b259a0ed31da9a015

commit e022b8b94971d07b93ed758b259a0ed31da9a015
Author: tsergeant <tsergeant@chromium.org>
Date: Tue Aug 09 02:52:14 2016

MD WebUI: Simplify cr-shared-menu exit animation

The current menu exit animation has the menu fade out while shrinking
width and height. However, the shrinking is barely visible and causes
visual glitches when quickly closing/reopening the menu.

This change does not completely fix either of the linked bugs, but it
greatly lessens their effect.

BUG= 632251 , 631840 
CQ_INCLUDE_TRYBOTS=master.tryserver.chromium.linux:closure_compilation

Review-Url: https://codereview.chromium.org/2222013003
Cr-Commit-Position: refs/heads/master@{#410553}

[modify] https://crrev.com/e022b8b94971d07b93ed758b259a0ed31da9a015/ui/webui/resources/cr_elements/cr_shared_menu/cr_shared_menu.js

The CL in #9 seems to reduce the amount of craziness that can happen when repeatedly opening and closing the menu. It still doesn't completely solve the problem, but I'm reducing the priority to not block launch.

The menu no longer has an animation, so this issue is obsolete.