Emulator

Game Name?

Mega Man Network Transmission - GREE08
Metal Gear Solid: The Twin Snakes - GGSEA4
F-Zero GX - GFZE01
Super Mario Sunshine - GMSE01

What's the problem? Describe what went wrong in few words.

While D3D correctly emulates Point/Line-Width, OpenGL does not. The solution to this is to implement geometry shaders in OpenGL to handle the situations where it is necessary.

Playing MegaMan Network Transmission and observing spawn/death animations, the rain in F-Zero GX's Thunder tracks at higher IRs, Metal Gear Solid Twin Snakes Minimap at higher resolutions, Super Mario Sunshine's expanding loading bubbles at higher resolutions.

Examples:

MegaMan Network Transmission OGL -> http://i.imgur.com/Dci6pq6.jpg
MegaMan Network Transmission D3D -> http://i.imgur.com/PJuEyqR.jpg

Super Mario Sunshine Loading -> http://i.imgur.com/nxKdy9H.png

Does using an older version of Dolphin solve your issue? If yes, which
versions of Dolphin used to work?

Older versions of Dolphin do not work; as far as I can tell this has never been implemented.

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

Core i5 3570K, GTX 760, Radeon HD5850, Windows 7 x64