The user manual is talking about embed tags on this page: http://unity3d.com/support/documentation/Manual/HTML%20code%20to%20load%20Unity%20Web%20Player%20content.html
I’m not sure about using the embed tag part since it has been deprecated and therefore isn’t valid for those following the w3 standard.
Are there any known issues when omitting those embed tags?
Just because something is deprecated doesn’t mean all browsers/versions work without it. I don’t know of any specific issues but you really ought to include them for safety until you (or someone) does a full and proper pass to ensure that all browsers work seamlessly and 100% correctly with only the object tag.
Of course the decision is ultimately up to you and what browsers/versions you want to target and what those configurations support. But for broad-scope support I’d say that both object and embed tags should be used.
Standards != functional reality 
Got it! 
Thanks!
I do agree. I would like to get rid of EMBED too.
PWETTY PLZ! Make Unity work from HTMLObjectElement!