Few months ago, the car started to shift really rough, N-D, 1-2, 2-3 etc. and takes long time to shift, however, it went away on its own after about 100 miles. Recently, I changed the trans fluid and filter, shifts are definitely smoother, but it seems to randomly delay shifting 1-2 and 2-3.

Now I went underneath the car and noticed the rear trans mount has a crack on it. Is it possible that previous harsh shifts tore down the mount and that'* why it seemed to disappear? What causes delayed random delayed shifts? And, finally, how do I read the trans codes on windows or iPhone using elm adapter? iOBD2 doesn't seem to read trans codes

How many miles on your car now?
From the heat varnish build ups, this can cause solenoids/check balls to get sticky in the valve body.
I also have a 4t-65e and didn't want to rebuild the valve body, even with similar hard shifts.
I bought some Seafoam Trans Tune & added a half a can, which is a great cleaner and after 1000 miles dropped the pan again & installed a TransGo shift kit into the accumulator.
Another new filter with Dexron 6,the latest spec'd GM fluid was utilized.
The P1811 code for delayed shifts was present, and went away after installing the shift kit.
See this link: https://www.gmforum.com/2000-2005-90...-4t65e-306901/
You will want to replace the trans mount and scan for codes. Also check the front mount under the hood carefully for cracks.
Post the codes once you have them please..
I have access to a Snap On Ultra which can read all stored codes, but as far as Mobile apps, hopefully others can chime in about that.
Still 50,000 miles later my 4T-65E is still going strong!

Does your ELM read data? If yes, then there are no transmission codes set....

Thanks guys for your replies! Mileage as it occurred was around 90x k miles. It turned out to be dirty MAF. I sprayed a little bit on the MAF, let it dry and installed it back and what do you know, shifts were normal again.
On a side note, my Elm scanner didn’t show any transmission codes.