Emulator

Reported that...
"This can be lessened (not fixed) by setting the backend to Direct3D and the Internal Resolution to Native."
...but that may not be accurate.

Nope also happens with single-core.

Using the debug GUI For Dolphin 5.0-13242, I tried turning off all of the available parts of JIT individually, or altogether, and then loaded a save state of the level select, and loaded a level.
In all cases this did not outright eliminate the white flickering issue, some parts being disabled could either increase or decrease the frequency of the flickering whilst others had no observable effect.
Using JIT LoadStore Off, the frequency of the white flicker could be reduced to one frame every few seconds, reduced from multiple frames per second.

Observed influences:

• JIT Block Linking Off: No observable change
• Disable JIT Cache: Emulation does not boot
• Disable Fastmem: Greatly reduced flickering before dropping a piece into water, greatly increased afterwards when puzzle/water surface resets
• JIT Off (JIT Core): Greatly reduced frequency
• JIT LoadStore Off: Greatly reduced frequency
• JIT LoadStore Ibzx Off: No observable change
• JIT LoadStore IXz Off: Greatly increased frequency
• JIT LoadStore Iwz Off: Greatly increased frequency
• JIT LoadStore Floating Off: Increased frequency
• JIT LoadStore Paired Off: No observable change
• JIT FloatingPoint Off: Greatly increased frequency
• JIT Integer Off: Greatly increased frequency
• JIT Paired Off: No observable change
• JIT SystemRegisters Off: No observable change
• JIT Branch Off: Greatly increased frequency
• JIT Register Cache Off: No observable change

Some additional notes:

• Dropping a piece into the water will restart the puzzle and reset the surface tension of the water to an idle low-amplitude ripple; the flickering issue may be more immediately observed afterwards, but can also occur whilst the water is rippling.
• The game is highly prone to an emulated system freeze when using frame advance or unpausing emulation whilst using JIT. Save states can be loaded when this occurs.

Further system info:

• CPU: Intel Core i5 4690K @ 3.9Ghz
• GPU: Nvidia GTX 770
• OS: Windows 10 64 bit
• RAM: 16 GB DDR3

I hope this information helps you with troubleshooting the issue.

With everything off, you're essentially running interpreter. So if there's still a difference, then we have a problem. We may need to see if there are occasional flickers on Wii.

Everything off appeared to be very close to interpreter, but emulation performance was around 7 to 10 FPS whilst still running JIT, as compared to the average 2.3 FPS using Interpreter Core.
There might be something I missed given a lack of familiarity with the debug interface.

My Wii system is currently in storage and would be difficult for me to set back up to check this on real hardware.
This video from 2010 appears to provide game footage captured from Wii hardware, though the recording is only 30 FPS so may not be reliable.
https://www.youtube.com/watch?v=5xdl2eBR2vM

I looked into this a little. This is also heavily affected by the CPU Clock Override setting.

This issue also disappears at 11% (79 MHZ) and below. The issue occurs most frequently at around 30% - 40% and drops off a little up to 100% where it still occurs less regularly.

I also checked previous revisions to see if there has been a regression and I have a bisect.

4.0-850 and newer up until now produce this issue.

4.0-846 and previous work just fine.

4.0-850 -> https://dolphin-emu.org/download/dev/a0a65a2906af132f6da04cf552812aac6ac5f20a/

Rechecked recently using Dolphin 5.0-20560.
I noticed a new CPU option under Settings -> Advanced called "Enable Write-Back Cache (slow)", and tried enabling it for Art of Balance.
Enabling this setting appears to resolve the water flashing white, at the expense of emulation performance.

Once you get to world B, the bowl is going absolutely crazy. Slightly over- or underclocking the CPU avoids the issue.