I have the same problems when I try to play Vampire the Masquerade: Bloodlines as well. I've tried different resolutions and troubleshooting the compatibility already.

A screenshot of the problem:
http://i.imgur.com/pIRl6.png
http://i.imgur.com/T7SSH.png
http://i.imgur.com/woBmu.png

Also, character models have lots of holes in them. Cutscenes are fine. Sound is fine. Game runs smoothly, no issues with framerate, just holes in the textures and certain textures getting way stretched out.

System Information
------------------
Time of this report: 7/31/2012, 01:06:14
Machine name: _____
Operating System: Windows 7 Home Premium 64-bit (6.1, Build 7601) Service Pack 1 (7601.win7sp1_gdr.120503-2030)
Language: English (Regional Setting: English)
System Manufacturer: Dell Inc.
System Model: Inspiron M5030
BIOS: BIOS Date: 01/09/10 15:17:22 Ver: 08.00.10
Processor: AMD Athlon(tm) II P360 Dual-Core Processor (2 CPUs), ~2.3GHz
Memory: 3072MB RAM
Available OS Memory: 2812MB RAM
Page File: 2483MB used, 3138MB available
Windows Dir: C:\Windows
DirectX Version: DirectX 11
DX Setup Parameters: Not found
User DPI Setting: Using System DPI
System DPI Setting: 96 DPI (100 percent)
DWM DPI Scaling: Disabled
DxDiag Version: 6.01.7601.17514 32bit Unicode

Display Devices
---------------
Card name: ATI Mobility Radeon HD 4200 Series
Manufacturer: Advanced Micro Devices, Inc.
Chip type: ATI display adapter (0x9712)
DAC type: Internal DAC(400MHz)
Device Key: Enum\PCI\VEN_1002&DEV_9712&SUBSYS_04871028&REV_00
Display Memory: 1402 MB
Dedicated Memory: 252 MB
Shared Memory: 1149 MB
Current Mode: 1366 x 768 (32 bit) (60Hz)
Monitor Name: Generic PnP Monitor
Monitor Model: unknown
Monitor Id: AUO22EC
Native Mode: 1366 x 768(p) (60.008Hz)
Output Type: Internal
Driver Name: aticfx64.dll,aticfx64.dll,aticfx32,aticfx32,atiumd64.dll,atidxx64.dll,atiumdag,atidxx32,atiumdva,atiumd6a.cap,atitmm64.dll
Driver File Version: 8.17.0010.1124 (English)
Driver Version: 8.961.0.0
DDI Version: 10.1
Driver Model: WDDM 1.1
Driver Attributes: Final Retail
Driver Date/Size: 4/5/2012 19:20:04, 1067520 bytes
WHQL Logo'd: Yes
WHQL Date Stamp:
Device Identifier: {D7B71EE2-D452-11CF-FC77-8D24BEC2C535}
Vendor ID: 0x1002
Device ID: 0x9712
SubSys ID: 0x04871028
Revision ID: 0x0000
Driver Strong Name: oem15.inf:ATI.Mfg.NTamd64.6.1:ati2mtag_RS880M:8.961.0.0:pci\ven_1002&dev_9712
Rank Of Driver: 00E62001
Video Accel: ModeMPEG2_A ModeMPEG2_C
Deinterlace Caps: {6E8329FF-B642-418B-BCF0-BCB6591E255F}: Format(In/Out)=(YUY2,YUY2) Frames(Prev/Fwd/Back)=(0,0,1) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_PixelAdaptive
{335AA36E-7884-43A4-9C91-7F87FAF3E37E}: Format(In/Out)=(YUY2,YUY2) Frames(Prev/Fwd/Back)=(0,0,0) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_BOBVerticalStretch
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(YUY2,YUY2) Frames(Prev/Fwd/Back)=(0,0,0) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY
{6E8329FF-B642-418B-BCF0-BCB6591E255F}: Format(In/Out)=(UYVY,UYVY) Frames(Prev/Fwd/Back)=(0,0,1) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_PixelAdaptive
{335AA36E-7884-43A4-9C91-7F87FAF3E37E}: Format(In/Out)=(UYVY,UYVY) Frames(Prev/Fwd/Back)=(0,0,0) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_BOBVerticalStretch
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(UYVY,UYVY) Frames(Prev/Fwd/Back)=(0,0,0) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(YV12,0x32315659) Frames(Prev/Fwd/Back)=(0,0,0) Caps=
{3C5323C1-6FB7-44F5-9081-056BF2EE449D}: Format(In/Out)=(NV12,0x3231564e) Frames(Prev/Fwd/Back)=(0,0,2) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_PixelAdaptive
{552C0DAD-CCBC-420B-83C8-74943CF9F1A6}: Format(In/Out)=(NV12,0x3231564e) Frames(Prev/Fwd/Back)=(0,0,2) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_PixelAdaptive
{6E8329FF-B642-418B-BCF0-BCB6591E255F}: Format(In/Out)=(NV12,0x3231564e) Frames(Prev/Fwd/Back)=(0,0,1) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_PixelAdaptive
{335AA36E-7884-43A4-9C91-7F87FAF3E37E}: Format(In/Out)=(NV12,0x3231564e) Frames(Prev/Fwd/Back)=(0,0,0) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY DeinterlaceTech_BOBVerticalStretch
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(NV12,0x3231564e) Frames(Prev/Fwd/Back)=(0,0,0) Caps=VideoProcess_YUV2RGB VideoProcess_StretchX VideoProcess_StretchY
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(IMC1,UNKNOWN) Frames(Prev/Fwd/Back)=(0,0,0) Caps=
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(IMC2,UNKNOWN) Frames(Prev/Fwd/Back)=(0,0,0) Caps=
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(IMC3,UNKNOWN) Frames(Prev/Fwd/Back)=(0,0,0) Caps=
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(IMC4,UNKNOWN) Frames(Prev/Fwd/Back)=(0,0,0) Caps=
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(S340,UNKNOWN) Frames(Prev/Fwd/Back)=(0,0,0) Caps=
{5A54A0C9-C7EC-4BD9-8EDE-F3C75DC4393B}: Format(In/Out)=(S342,UNKNOWN) Frames(Prev/Fwd/Back)=(0,0,0) Caps=
D3D9 Overlay: Not Supported
DXVA-HD: Not Supported
DDraw Status: Enabled
D3D Status: Enabled
AGP Status: Enabled

Try to install fresh video driver, directx. But I think you did.
Maybe gpu's overheat. MSI Afterburner plots graph of temperature for example.

I can play much more demanding games, for example TES IV: Oblivion with no graphical issues at all. I don't think heating is the issue.

This is the first time I've seen anything like this. Have you tried using 3D Analyser to emulate another card? Might be worth a shot.

I was having the exact same issue and couldn't find many responses, but I played around with my graphics card settings and managed to fix it.

I'm running off an ATI Radeon 3000 Graphics card.

After updating the latest driver, I went to the advanced settings in the AMD Control Center. I went to the 3d Application Settings under gaming and enabled adaptive anti-aliasing..apparently it wasn't active before. I"m assuming the AMD control centers are pretty similar.

The game gets slightly more laggy every once in awhile, but other than that it runs perfectly and looks 100 times better. The lag could probably be fixed if I went to the in-game settings and experimented, but it hasn't greatly affected gameplay yet. It was almost unplayable with the texture holes and glitches.

Hope that fixes it for you.