Thanks for taking the time to report this!

Which exact version of TimedMediaHandler are you using? Which exact version of MediaWiki? Which Firefox and Chrome version on which operating system? Any public testcase?

I am using MediaWiki 1.25.2. The TimedMediaHandler version is REL1_25: rev c4274e4. Firefox 40.0.2 and Chrome 44.0.2403.155. On Chrome there is a similar problem except it does not have the notice. The OS is Windows 10. I have not yet made a public testcase. I also tested using Firefox 40.0 on Ubuntu 14.04 and same problem.

Server operating system is Ubuntu 14.04.1 Server

The following comes from a Firebug debug console:

jQuery.fn.embedPlayer :: 1
processEmbedPlayers:: playerSet: Object[video#mwe_player_0.kskin]
processEmbedPlayers:: Do: 1 players 
EmbedPlayer:: addElement:: mwe_player_0
EmbedTypes::detectPlayers running detect
(19) EmbedTypes::addJavaPlayer: adding cortadoPlayer
EmbedPlayer::trigger:embedPlayerUpdateMediaPlayersEvent
processEmbedPlayers::runPlayerSwap::mwe_player_0
EmbedPlayer: initEmbedPlayer: 950
EmbedPlayer::init:mwe_player_0 duration is: 310.294
EmbedPlayer::mediaElement:init:mwe_player_0
processEmbedPlayers::swapEmbedPlayerElement: mwe_player_0
processEmbedPlayers::trigger:: EmbedPlayerNewPlayer mwe_player_0
TimedText: init() 
EmbedPlayer::addPlayerElement :trigger startPlayerBuildOut:mwe_player_0
EmbedPlayer::checkPlayerSources: mwe_player_0
EmbedPlayer::setupSourcePlayer: mwe_player_0 sources: 2
EmbedPlayer::mediaElement::autoSelectSource
MediaElement::GetPlayableSources mimeFilter:undefined 0 sources playable out of 2
EmbedPlayer::showPlayerError
MediaElement::GetPlayableSources mimeFilter:undefined 0 sources playable out of 2
EmbedPlayer:updatePosterHTML::mwe_player_0
mw.PlayerControlBuilder: addWarningBinding: EmbedPlayer.ShowNativeWarning wm: For a better video playback experience we recommend an <a href="//www.mediawiki.org/wiki/Extension:TimedMediaHandler/Client_download" target="_blank">HTML5 video browser</a>.
EmbedPlayer:: setupSourcePlayer > player ready ( but with errors ) 
EmbedPlayer:: Trigger: widgetLoaded

A few questions:

• Is this a locally uploaded video or a video from Commons loaded via InstantCommons?
• What type is the video? Is it webm, ogg, or something else (eg have you enabled mp4 uploads or other non-standard config etc?)
• Have the derivative transcodes been successfully generated? (There should be a table at the bottom of the page listing them and their status.)

If it's a locally WebM video, and you don't have a job runner daemon configured to run the transcodes, you may be hitting the bug that original WebM sources didn't get loaded (T91431).

The video is a locally uploaded video, and is a WebM video. Transcodes are disabled. I recently tested using an ogg video and did not encounter the problem.

In T109150#1562791, @ComputeVictory wrote:

The video is a locally uploaded video, and is a WebM video. Transcodes are disabled. I recently tested using an ogg video and did not encounter the problem.

Aha, that definitely sounds like T91431 -- try manually applying the update from https://gerrit.wikimedia.org/r/#/c/231309/1/handlers/WebMHandler/WebMHandler.php

Or just download http://git.wikimedia.org/raw/mediawiki%2Fextensions%2FTimedMediaHandler.git/a9ef4642bbcdca339bc78ba7286bf0c86317f59a/handlers%2FWebMHandler%2FWebMHandler.php and drop it in place of handlers/WebMHandler/WebMHandler.php ... should do the job. :)