Speaking about T-34, there are some things that should be understood.
* The basic T-34 flaws were well understood even before the war. In 1941, the refined versio - T34M - was planned, with torsion suspencion replacing the outdated Christie one, three-man turret, ect. But the production of prototypes only started just before invasion, then the factory was evacuated and the whole project essentially dropped with no tank acually produced.
* USSR used tanks on much larger scale than other great powers of WW2 era. Soviet tanks played important role in both mechanized assaults and infantry support. Due to... problematic quality of Red Army indirect fire support, direct fire support was viewed as essential. So USSR was essentially forced to crunch out tanks constantly, putting quantity above all. The fact that T-34 was extremely good in both combat and industrial terms greatly helped the situation.
* While there were attempts to develope a new medium tank to replace T-34 - like experimental T-43, which turret serves as basic for T-34-85 upgrade, or lightened heavy tank KV-13 - they did not demonstrate sufficient superiority over T-34 to validate putting them into production. Sure, they were better, but not that better; and causing a delay in armor production to merely put a slightly better tank in service was a no-go for USSR.
* A new tanks woud most likely have teething troubles, which may cause a significant delays before they would be combat-ready. It took almost a year (1945-1946) to remedy all flaws found in IS-3, and IS-4 heavy tank was essentially so flawed that Soviet Army gave up on it after producing a small series.
* The T-44 tank was developed as T-34 replacement, and basically was everything Red Army wanted. But since the war was already closing, there were no point in rushing it into production.