Emulator

Game Name?
Well, "various".. Tested especially on those:

Super Paper Mario (SPM)
Mario Sports Mix (MSM)
New Super Mario Bros. Wii (NSMBW)
Mario & Sonic at the London Olympic Games (LOG) -minor-

Game ID?
Well, "various".. Tested especially on those:

R8PE01
RMKE01
SMNE01
SIIE8P -minor-

What's the problem? Describe what went wrong in few words.
Well, Distorted Graphics, see screenshots for more details.

SPM: Some of the nearby layer (for example in Flipside: the houses) are minory distorted (small dots in various places displaying a weird color)

MSM:Well, the characters' models at the start (Mario, Luigi, Peach and Bowser who holds Basket ball, Dodge ball, Volley ball and Hockey thing to be exact) are very distorted -didn't go into actual gameplay though.

NSMBW: the characters at the start running seems to be perfect, but the actual character in the Stage select (see screenshot) is very distorted.]

LOG: the models and sprites seems to be good, just the background (the sky) in some events, it has got small amount of dots but meh.

What did you expect to happen instead?
Normal?

Dolphin 3.5 and 3.5-367 are old versions of Dolphin that have
known issues and bugs, so don't report issues about them and test the
latest Dolphin version first.
Which versions of Dolphin did you test on?
The last version as of the time of this writing: 4.0-1707, x64
Does using an older version of Dolphin solve your issue? If yes, which
versions of Dolphin used to work?
yep, it does. The one I'm very sure about is 4.0-1146, x64 (sorry it is very old)

What are your PC specifications? (including, but not limited to: Operating
System, CPU and GPU)

Processor: Intel(R) Core(TM) i5-3317U CPU @ 1.70GHz
Installed memory (RAM): 4.00 GB (3.87 GB usable)
System type: 64-bit Operating System, x64-based processor
GPU: Intel(R) HD Graphics 4000

Are you using the 32 or the 64 bit version of Dolphin?
x64

Is there any other relevant information? (e.g. logs, screenshots,
configuration files)
SPM: http://s27.postimg.org/bbft0hjzn/R8_PE01_1.png
MSM: http://s22.postimg.org/or8r85blt/RMKE01_1.png
NSMBW: http://s15.postimg.org/50o0mrbzv/SMNE01_2.png, http://s15.postimg.org/hljwcfn97/SMNE01_3.png
LOG: It was so minor, that i skipped it.

And one last word please, don't assume my graphic card is so weak or anything. Things used to work on previous builds.