I ran into this issue today - specifically ActiveX not being recognized as available so Datasheet view didn't work on a list. (Edit 2014-07-10: This works to fix SharePoint 2013 pre-SP1 as well e. g. not being able to work with web parts in edit mode.)
There are two fixes to this on the client side, but they are both very big hammers:
You can add the site to the Compatibility List in IE ([gear] ->
Compatibility View Settings -> Enter URL,
Add). This is a big hammer because it actually applies to the entire DNS domain, which if SharePoint is one of many things in the DNS domain, is really bad. So this was no good for me.
You can add the site to the
Intranet zone and have the
Display Intranet Sites in Compability View checkbox turned on (also in
Compatibility View Settings). This impacts all sites in the zone, which will hurt sites in that zone that are not broken on IE11. So this was also no good for me.
I tried the different ASP.NET updates to update ASP.NET browser detection but that was all up to date, so that didn't help.
However, as a hunch, I decided that somewhere SharePoint was doing "User Agent Sniffing" - the timeframe of the code was right for that, and a very, very large number of IE11 compatibility issues come down to user agent sniffing. The user agent was changed on purpose for IE11 (ref: http://blogs.msdn.com/b/ieinternals/archive/2013/09/21/internet-explorer-11-user-agent-string-ua-string-sniffing-compatibility-with-gecko-webkit.aspx).
Since I can't work out where it's happening, and the whole web site on the server is dedicated to SharePoint 2010, I decided I would use a medium-sized hack-shaped hammer to fix this. The hack is to change the user agent being reported to SharePoint to make IE 11+ look like IE 8.0.
Steps you should follow to reproduce:
Install the URL Rewrite 2.0 module on the server if it's not already installed. (Current URL: http://www.iis.net/downloads/microsoft/url-rewrite but it's very easy to find).
Open the IIS Manager (the current one, not the IIS 6.0 legacy one).
Select the web site under
IIS section, open
Manage Server Variables select
View Server Variables....
When prompted with
Add Server Variable, enter
HTTP_USER_AGENT as the
Server variable name: and press
Back to Rules.
You are now back at the main
URL Rewrite context. Under
When prompted for
Add Rule(s) select
Blank rule under
Inbound rules and press
Create the rule as follows:
That's it, done. This worked for me - the datasheet view immediately worked correctly without my browser set for compatibility mode for the page beyond the automatic "act like IE 8" that seemed to happen without me doing anything.
You could conceivably also a rewrite rule to add the
IE=8 rendering meta tag into all ASPX responses as well - I haven't done that myself so I'm not documenting details here but it shouldn't be too hard to figure out from what I have here.
(edit 2014-07-10: added small missing step)