I think the semantic is slightly different. This makes sense:
[a] should(expression).throw(someError)

However, this is not really clear:
[b] should(expression).beRejected(someError)

Perhaps it would be better with:
[c] should(expression).beRejectedWith(someError)

Note that this method without an argument reads awkward as well. 

This might be a matter of preference, but [b] is the easiest thing to do as you stated.

We don't have to add it.  Just that some tests were written handle the rejected promise and then also checked the reason why.

Option [c] is ok if we make the arg required.

Option [c] means we have to fix the existing beRejected() assertion. Is it what we want?

Are you saying [c] would replace all existing current uses of beRejected()?  That wasn't my intent, but we could.  But then I would say beRejectedWith() would need to support no arg for the cases where we don't care. I'm ok with having both beRejected() and beRejectedWith(required).

There is still the option of not doing anything.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/9f0467f5ac93ea19f8ded30cf82fc68f538e7ad1

commit 9f0467f5ac93ea19f8ded30cf82fc68f538e7ad1
Author: hongchan <hongchan@chromium.org>
Date: Tue Jan 24 02:43:27 2017

This CL adds should().beRejectedWith() so you can specify the expected
error type.

BUG= 678723 
TEST=
LayoutTests/webaudio/unit-tests/audit.html
LayoutTests/webaudio/unit-tests/audit-failures.html

Review-Url: https://codereview.chromium.org/2654673003
Cr-Commit-Position: refs/heads/master@{#445617}

[modify] https://crrev.com/9f0467f5ac93ea19f8ded30cf82fc68f538e7ad1/third_party/WebKit/LayoutTests/webaudio/resources/audit.js
[modify] https://crrev.com/9f0467f5ac93ea19f8ded30cf82fc68f538e7ad1/third_party/WebKit/LayoutTests/webaudio/unit-tests/audit-expected.txt
[modify] https://crrev.com/9f0467f5ac93ea19f8ded30cf82fc68f538e7ad1/third_party/WebKit/LayoutTests/webaudio/unit-tests/audit-failures-expected.txt
[modify] https://crrev.com/9f0467f5ac93ea19f8ded30cf82fc68f538e7ad1/third_party/WebKit/LayoutTests/webaudio/unit-tests/audit-failures.html
[modify] https://crrev.com/9f0467f5ac93ea19f8ded30cf82fc68f538e7ad1/third_party/WebKit/LayoutTests/webaudio/unit-tests/audit.html