Moderator note
Not a Minecraft bug, this is a hardware issue.
Keyboards cannot necessarily record 3 random pressed keys at once, especially Laptop / Notebook / Wireless Keyboards have different keyboard matrix / CPUs compared to desktop keyboards.
There is nothing you can do to solve this except for switching to another keyboard that doesn't have this issue.
Cannot move left while holding the TAB and LSHIFT keys at the same time.
This occurs in all recent versions of the game (1.7.X, Snapshots)
Java 7 on Windows 8.1.
Related issues
is duplicated by
relates to
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Incomplete without further details, e.g OS, Java version.

Confirmed for me in 14w18a, but shift+any arrow doesn't work for me AT ALL, due no doubt to the fact that I use the keypad arrows to move. I never noticed before because I use the keypad for crouch, and every other button too (isn't that the point of gaming with the keypad arrows? enough buttons beside the arrows to handle everything?)
So doing a PROPER playtest (setting the movement and crouch to defaults): cannot reproduce. But for anyone using the keypad for movement there's a bug there.

I misstyped when I made the post, it's TAB not ALT, sorry.

Ah ok, retesting...
Confirmed in 14w18a (yes with default controls). Why only left is affected but not the other 3 directions is beyond me.

Yeah I don't get that either.

Not a Minecraft bug, this is a hardware issue.
Keyboards cannot necessarily record 3 random pressed keys at once, especially Laptop / Notebook / Wireless Keyboards have different keyboard matrix / CPUs compared to desktop keyboards.
I have a "normal" 104 key keyboard and any combination of three keys out of TAB/LSHIFT/CTRL plus movement keys is working here fine on Windows 7.

honestly I'm a bit sure that this is an issue with minecraft's recieving of inputs, because this is an issue for me as well
Cannot reproduce.