I note I can also replicate this in incognito mode

Reminds me of T151770.

For anyone affected by log-in problems who wants to help track them down:

Please see and follow https://www.mediawiki.org/wiki/Manual:How_to_debug/Login_problems and report back here. Thanks!

Does it persist after clearing cookies for the wiki domain? No existing cookies in incognito

When logging in in incognito mode? Doesn't work either
When logging in with a different kind of browser? Broken in FF and Chrome
If you use any ad blockers or browser privacy add-ons, are they blocking anything? No Does it work if you turn them off? No because it's not on
Does it affect all user accounts, or just one? Unknown, definitely more than 1 account
Does the "remember me" flag make any difference? (Clear cookies before attempts.) No
If the problems are happening on a WikiMedia wiki, try logging in on another wiki, preferably one that does not share a second-level domain name (so if the problem happens on xy.wikipedia.org, try for example xy.wiktionary.org). Other wikis seem fine (not all tested obviously)

Probably needs a HAR file at this point

I can reproduce this when using mr.wikipedia.org in mr, however, when I try to login with interface switched into English, I have no problems with logging in. @Reedy or anyone having this issue, can you please try to verify this theory?

In T226754#5292040, @Urbanecm wrote:

I can reproduce this when using mr.wikipedia.org in mr, however, when I try to login with interface switched into English, I have no problems with logging in. @Reedy or anyone having this issue, can you please try to verify this theory?

Lol, yes, I can confirm

I actually tried that when debugging on IRC to see the error message, and was able to login. Forgot about it completely... :)

Okay, I think this is caused by local content of mediawiki:Loginprompt. When I copied loginprompt from mrwiki to test.wikipedia.org, I reproduced the issue there as well. When I reverted my test on test.wikipedia, issue disappeared. @Reedy, can you delete MediaWiki:Loginprompt from mrwiki to test this theory there as well? Thanks!

In T226754#5292057, @Urbanecm wrote:

Okay, I think this is caused by local content of mediawiki:Loginprompt. When I copied loginprompt from mrwiki to test.wikipedia.org, I reproduced the issue there as well. When I reverted my test on test.wikipedia, issue disappeared. @Reedy, can you delete MediaWiki:Loginprompt from mrwiki to test this theory there as well? Thanks!

Deleted and confirmed working

the contents were as below, since 12:54, 26 July 2014

[[File:Marathi Wikipedia ULS.webm|thumb|उजवे|300px|मराठीत टाईप करण्यासाठी, ह्या व्हिडिओ क्लिपेत दाखवल्या प्रमाणे, मराठी आणि नंतर अक्षरांतरण पर्याय निवडा, अथवा इनस्क्रिप्ट साठी 'मराठी लिपी' पर्याय, तुम्ही तुमची व्यक्तीगत युनिकोड टायपींग पद्धती वापरू शकता. Click on the '''cc'' to change the subtitle languages to Marathi, English, Sanskrit, Kokani,Ahirani.]]
{{SITENAME}}मध्ये सनोंद-प्रवेशासाठी  स्मृतिशेष सक्षम (कुकिज एनेबल)असणे आवश्यक आहे.

IMHO there is no reason to expect this message to be comfortable with holding a video. I'd consider it a local configuration error, now fixed. As a MediaWiki bug report, I'd consider it invalid/wontfix.

Sounds like it might be related to T226840. One of the background requests during the login process may be failing for the same reason (header explosion) and thus cause cookies to be lost.

Probably not worth putting much effort into, now that the video player is about to be replaced.