I also have dotnet 4.5 installed, but it doesn't create any problems with GF for me. Looking at the GF exe/assembly it seems that GF uses dotnet v2.0.50727. If you know a little about dotnet, the major versions like 2.x, 3.x and 4.x coexist; actually you need to have the lower major installed because the latter ones are supersets (except for 1.x which isn't included in 2.0.) The big snafu is indeed with 4.5, which has some incompatible changes with 4.0 and it's not installed as a superset but replaces 4.0. But GF using 2.0 doesn't seem to be affected by this 4.0/4.5 issue... at least on my computer.
So, I don't know what to say other than make sure you have all the updates for dotnet 2.0 pulled from/via Windows Update. (There are separate updates for the major dotnet releases there.) These are installed automatically on Windows 7 (which comes with dotnet 3.5 and all prior major versions, including 2.0, but not with dotnet 1.x, which was a different beast) unless you disable/disallow updates for dotnet on purpose.
One thing you could try is running "sfc /scannow" from the admin command prompt to make sure your Windows installation (including the dotnet dlls) isn't corrupt somehow.
You can find out what dotnet version patches you have installed using the sample code from http://msdn.microsoft.com/en-us/library/hh925568.aspx and http://msdn.microsoft.com/en-us/library/hh925567(v=vs.110).aspx
This is what I have according to the 1st program:
v2.0.50727 2.0.50727.5420 SP2
v3.0 3.0.30729.5420 SP2
v3.5 3.5.30729.5420 SP1
v4
Client 4.5.50938
Full 4.5.50938
v4.0
Client 4.0.0.0
And according to the 2nd one which lists patches:
Microsoft .NET Framework 4 Client Profile
KB2468871 Update for Microsoft .NET Framework 4 Client Profile (KB2468871)
KB2468871v2
KB2478063 Update for Microsoft .NET Framework 4 Client Profile (KB2478063)
KB2533523 Update for Microsoft .NET Framework 4 Client Profile (KB2533523)
KB2544514
KB2600211
KB2600217 Update for Microsoft .NET Framework 4 Client Profile (KB2600217)
Microsoft .NET Framework 4 Extended
KB2468871 Update for Microsoft .NET Framework 4 Extended (KB2468871)
KB2468871v2
KB2478063 Update for Microsoft .NET Framework 4 Extended (KB2478063)
KB2533523 Update for Microsoft .NET Framework 4 Extended (KB2533523)
KB2544514
KB2600211
KB2600217 Update for Microsoft .NET Framework 4 Extended (KB2600217)
Microsoft .NET Framework 4.5
KB2729460
KB2737083
KB2742613
KB2748645
KB2750147
KB2789648
KB2794055
KB2804582
KB2805221
KB2805226
KB2823493
KB2835622
KB2858725
KB2861193
KB2861208
KB2872778
Microsoft .NET Framework 4.5.1
KB2898869 Security Update for Microsoft .NET Framework 4.5.1 (KB2898869)
KB2901126 Security Update for Microsoft .NET Framework 4.5.1 (KB2901126)
KB2931368 Security Update for Microsoft .NET Framework 4.5.1 (KB2931368)
Strangely, it doesn't list any patches for the versions before 4, although I think I have some of those too. YMMV as they say.