I got my H1B transfer approved to a new employer, with valid I-797 and I-94, but my passport still has an H1B stamping from my previous employer which has not yet expired. Can I still enter the US without any concerns?
Yes, visa is just a travel document required to enter the US and is independent of employer even if it has employer name on it. So as far as it is valid you can use it with new employer I-797.