do they fail every time? there's a low timeout that can hit a lot. I've posted a CL for it.

They fail every time for me. I'm not sure if it's actually a timeout thing in these cases?

they still fail after https://chromium-review.googlesource.com/963901 ?

They seem to :( 
 display-img-dimensions
    assertEQ: hterm_terminal_tests.js:405: 4 !== 5

The following revision refers to this bug:
  https://chromium.googlesource.com/apps/libapps/+/547ea6d049806fda397381072cb40d6427a4ef31

commit 547ea6d049806fda397381072cb40d6427a4ef31
Author: Raymes Khoury <raymes@chromium.org>
Date: Tue Jun 12 23:48:04 2018

hterm: Fix floating point rounding error in Terminal.dimensions tests

There can apparently be floating point error with the rounding of
dimensions on different platforms. Round values in these tests to
avoid test failures.

Bug: 847122
Change-Id: Ibc03b4351a292d1cbeea13f2dae050ed37438b3d
Reviewed-on: https://chromium-review.googlesource.com/1080352
Reviewed-by: Mike Frysinger <vapier@chromium.org>
Tested-by: Raymes Khoury <raymes@chromium.org>

[modify] https://crrev.com/547ea6d049806fda397381072cb40d6427a4ef31/hterm/js/hterm_terminal_tests.js

is this fixed now ?

No, the image tests are still failing for me. Also the dimensions test now only seems to pass after I resize the window..

hterm.Terminal.Tests
  dimensions
    assertEQ: hterm_terminal_tests.js:101: 79 !== 80

 display-img-dimensions
    assertEQ: hterm_terminal_tests.js:512: 4 !== 5
    ERROR: FAILED

I had a brief look into the dimensions test. It's seemingly related to rounding error in the round trip between creating a terminal with a specific size (80 cols) and then getting the client dimensions of the screen node, which don't exactly correspond.