Result: the video does not display correctly鈥攊t has extra spacing around the video that shouldn't be there.

Seen at https://design5279.wordpress.com/ (wpcom simple) with the Twenty Seventeen theme applied using Firefox 57.0 on Mac OS X 10.13.1.
I expected that embedding a video into a widget area using the Video Widget would result in a video sized correctly.
Videos embedded into a widget area using the Video Widget result in a black box with extra spacing where it should not be.
Internal refs:
/hat tip @darnelldibbles for the original Trac ticket 7957-wpcom and forums report link 882990-f.
This is how the sidebar looks when a video URL is added via the Video Widget:

And when set to full screen:

/hat tip @kristarella for the chat report at 951288-hc.
I tested with several themes and different YouTube videos and all had excess grey space in the widget, and a tiny video in the full screen view.
/hat tip @vparkhere for the Trac ticket at 7915-wpcom and the email report at 3319036-t.
/hat tip @rachelmcr for testing and confirming the issue at 7957-wpcom #comment:3.
/hat tip @laurelfulford for the live chat at 957298-hc and the email follow-up at 778822-zd-woothemes.
/hat tip @scosgro for the testing (theme Pique) and the email report at 773311-zd-woothemes.
/hat tip @otpidusprime for the email report at 777316-zd-woothemes.
/hat tip @kathrynwp for the forums report at https://en.forums.wordpress.com/topic/dara-theme-no-full-screen-on-video-widget
/hat tip @edequalsawesome for the chat report at 951337-hc and the email follow-up at 779731-zd-woothemes and for noting the theme name! (Theme: Broadsheet)
I tested this and was able to replicate it with the Broadsheet theme, but the full-screen video player worked as expected when I tested with Twenty Seventeen.
/hat tip @scosgro for the chat report at 56811-hc. (Theme: Big Brother)
/hat tip Pratik for the email report at 787263-zd-woothemes. (Theme: Heart and Style)
/hat tip @hacchism for the email report at 787263-zd-woothemes. (Theme: Heart and Style)
/hat tip @eduardozulian for noting a previous report is checking back in at 1006523-hc.
/hat tip @adelineyaw for the email report at 795115-zd-woothemes.
/hat tip @cscheer for the report in Slack at p1510938318000593-slack-triage.
/hat tip @katinthehatsite for the chat report at 1038621-hc and for noting a workaround!
As a temporary workaround to fix the size, I have added text widget + embedded the video through a shortcode eg. [youtube]
/hat tip @wynwinfor the chat report at 1045426-hc and the follow-up ticket at 803337-zd-woothemes.
/hat tip Tiffany V for the chat report at 957298-hc and the follow-up email at 778822-zd-woothemes.
Marked 4735-wpcom as a duplicate.
This is addressed by r165801-wpcom and r165809-wpcom for .com sites. #8225 for Jetpack sites. Will close this issue when #8225 gets merged.
This still appears to be affecting Jetpack (and Atomic) sites running Radcliffe 2.
Reported here: 816487-zd-woothemes
I tested a Youtube video in the Video Widget on a WordPress.com Simple, WordPress.com Atomic, and a self hosted (Pressable) Jetpack site. All three were running Radcliffe 2.
The Simple site worked fine - Atomic and Jetpack still displayed the video thumbnail sized in full screen mode.
cc @oskosk
Thanks @chad1008 will check.