This is from my 9 months ownership of the Lumia 620.
1. Battery rapidly drains every now and again and this is when I'm not even using it a lot.
The battery life of the Lumia 620 is mediocre. It drains like water when the data connection is active but when I shut it off, it can last for 3-4 days. With data, I can make it last for around 6-8 hours a day. Only with WiFi, a day or 2 is possible.
2. The phone freezes up on occasion and I need to take the battery out
Nope, never happened to me.
3. Scroll up to unlock the lock screen messes up far to often and doesn't let me scroll the screen all the way up to unlock. I need to turn the screen off and on for it to work properly.
I also experience this issue, and this seems to also affect call answering sometimes. When I pull the phone out of my pocket, the slider messed up. I have to lock and unlock the screen to make it work again. It's pretty annoying!
4. I get an error saying the SD card has been removed when it hasn't.
Never had this, but I did have some sort of error when I put in the SD card for the first time and all I need to do is to format the card from the phone and it works like a charm afterwards!
5. Music app is slow and I mean slow. I have like 20GB of music on an SD card. Ill load the app up and select a song, the song plays but it takes up to 20 seconds for the screen to flip over to the screen which shows the song that currently playing, during this time I cant do anything with the phone, not even lock it. Really poor in my eyes.
My music collection in the phone is somewhere around 2GB and all of them are on my SD Card. Seems to be loading fine on mine. Maybe you need to upgrade to a higher class SD Card because I've been hearing about performance issues with SD Card across WP8 phones..
6. Screen becomes unresponsive from time to time and I have to lock and unlock the phone for it to become responsive again.
This has been discussed a long time ago and the culprit is the grounding issue with the back cover.
7. If phone is locked and I hold down there camera button the lag is silly the time it takes to open the camera and take a photo is far too long, slow.
This is also related to SD Card..
EDIT:
I've since updated my phone to Amber and everything seems to be fine. The frequency of app crashes are getting lesser and lesser, improved overall performance and the features it brought in is just magnificent! However, I still have an issue with the phone call answering.