Able to reproduce this on the latest M-53(53.0.2750.0) on Linux Ubuntu 14.04 as well.

@Sindhu: Please update the bisect here.

CHANGELOG URL:      
 https://chromium.googlesource.com/chromium/src/+log/a6c06f926e897df19c873bf5be07cd87d51b8c1b..7ba991af2ed157f2c8ef8ad1855bfaa620f34da6

Suspecting https://codereview.chromium.org/1907103002 from changelog

@thomasanderson: Please confirm the issue and help in re-assigning if it is not related to your change.

I can confirm that this problem started occuring at change https://codereview.chromium.org/1907103002

This change appears to expose an existing issue in chrome.  It appears we blacklist scale factors > 130% here:
https://code.google.com/p/chromium/codesearch#chromium/src/chrome/browser/ui/libgtk2ui/gtk2_ui.cc&sq=package:chromium&l=1391

This is why it works with a scale factor of 1.25 but not 1.38.  Passing to oshima (a reviewer of the commit from the git-blame).

Chrome currently requires restart when DSF changes. This has been this way, and I don't have time to change this behavior. I can change it so that it always use the same scale for its lifetime.

That sounds like a good fix to me.

This issue is marked as Beta blocker, please resolve asap. 

M52 will be promoted to Beta on 06/01, please have the fix baked in canary and merged to 2743 branch before 05/30 Monday.

Issue still reproduced on latest M 53 i.e. 53.0.2753.0 and 52.0.2743.19.

thomasanderson/oshima : Could you please take a look into this and update further.

oshima@ Are you making the change described in #5 ?

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/52c96f45954fb726585acd0bac295d801728b22e

commit 52c96f45954fb726585acd0bac295d801728b22e
Author: oshima <oshima@chromium.org>
Date: Wed Jun 01 17:30:28 2016

Keep using the same DPI scale

* Dynamic DSF change is not supported/tested on linux. Jus make sure that it uses the same scale unless restarted.

BUG= 615353 
R=thomasanderson@chromium.org

Review-Url: https://codereview.chromium.org/2022383002
Cr-Commit-Position: refs/heads/master@{#397171}

[modify] https://crrev.com/52c96f45954fb726585acd0bac295d801728b22e/chrome/browser/ui/libgtk2ui/gtk2_ui.cc

Do you think the CL is safe to be merged before baking in canary?

This does not seem to be super urgent (as restarting chrome fixes), so we can wait a bit more.

Great, we will verify in today's canary and update the thread.

Your change meets the bar and is auto-approved for M52 (branch: 2743)

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/ee319470677620e163b9406ca2fc2743c9c2c344

commit ee319470677620e163b9406ca2fc2743c9c2c344
Author: Mitsuru Oshima <oshima@chromium.org>
Date: Thu Jun 02 21:40:35 2016

Keep using the same DPI scale

* Dynamic DSF change is not supported/tested on linux. Jus make sure that it uses the same scale unless restarted.

BUG= 615353 
R=thomasanderson@chromium.org

Review-Url: https://codereview.chromium.org/2022383002
Cr-Commit-Position: refs/heads/master@{#397171}
(cherry picked from commit 52c96f45954fb726585acd0bac295d801728b22e)

Review URL: https://codereview.chromium.org/2036693003 .

Cr-Commit-Position: refs/branch-heads/2743@{#199}
Cr-Branched-From: 2b3ae3b8090361f8af5a611712fc1a5ab2de53cb-refs/heads/master@{#394939}

[modify] https://crrev.com/ee319470677620e163b9406ca2fc2743c9c2c344/chrome/browser/ui/libgtk2ui/gtk2_ui.cc

Checked the issue on 53.0.2757.0 dev ,Ubuntu 14.04 and is working fine.i.e; Able to click on close/wrench menu/star icon after changing scale to 1.38.

thanks for the update.

Tested the issue on Linux Ubuntu 14.04 using chrome version 53.0.2757.0.able to click on ment and star icons after changing the scale factor from 1 to 1.38
Adding TE-Verified label.

Thnaks,

If there is no pending work, could you please mark as fixed.

Tested the issue on Ubuntu 14.04 using 52.0.2743.33.Observed that on changing the scale factor from 1 to 1.38, able to click on close/wrench menu/star icon.

Marking it as TE-Verified-M52.