Not quite those issues, but the shown variations, clicking on them doesn't produce a sound when the pieces move.
Also clicking on the variation, it's sort of locked for some seconds until there is a reaction. I'm assuming it's something new to stop the evaluation bar from making huge jumps? Maybe there could be some visual cue that it's locked and still calculating or some kind of "autoplay" so the variation line plays out itself without having to click
Wonky game analysis
@solomonwu This is a bit of a long shot suggestion, but is your browser up to date?
If not, try updating it and maybe clearing your cache of temporary files. Doubtful that would be a quick fix, but it's worth a try. Would take less than a minute to do.
What is your screen resoltion? any change you are on a very very small screen? Can you perhaps submit this as a bug when it happens to you next time? That will capture some extra data for us from behind the scenes:

@Jonani I am very sure that my bowser is up to date.
@jdcannon my screen is regular. Screen resolution is normal.
I have also submitted a bug report.
Yo! I figured out the issue.
If you turn arcade animation off, it will fix it for you. We are working to make arcade work correctly.
@jdcannon What's the difference between the animation selections? I've come across this setting befoe, but wasn't sure what it's purpose was, so was unsure what to select as my choice.

Choose "arcade" then go play a game of bullet chess. You will very quickly answer your own question
No offense, but you're kinda basically asking him to lose a game technically
@Jonani, if you decide to try it, make sure the game is unrated
@sougataghosh Thank you for the warning about "arcade mode". I appreciate the heads up!
Also, the GIF you posted reminds me of this skit from SNL. No racial pun intended, because the skit is titled "Black Jeopardy", afterall. Seeing Kenan Thompson reminded me of the skit.
https://www.youtube.com/watch?v=O7VaXlMvAvk
Choose "arcade" then go play a game of bullet chess. You will very quickly answer your own question
@jdcannon I'll ponder your offer and let you know if I decide to "walk on the wild side" and try arcade mode in Bullet haha. Maybe I'll find a sympathetic and understanding opponent? ![]()
I did my own test and made a video for you: http://somup.com/cq11qDnJsB
You can get some other fanciness from it too when for example you checkmate.
Here you go 
So on google chrome, and this has been happening for a while(past week), there are three things that don't seem right.
#1: The arrows which show where a piece has moved is moved to the point where it is unclear or not even correct.
#2: The piece evaluation(+3 for black, +1 for white, white has a knight, etc...) is on the board.
#3: The photo image for each player is on the board.