Lens cover stays open

Sure it is, and repair isn't that hard. See this link for tips on repair of sticky automatic lens covers. Recommend reading the reader's comments section of the link for additional tips. Especially pay attention to the vacuum cleaner tip.

It sounds like a problem with the firmware in the camcorder itself. As an authorized Sony repair person, I have gotten no technical bulletin on this model. The firmware is preloaded into the microprocessor IC. You will need to have this unit looked at by an authorized Sony repair center who specializes in camcorder repairs or send the unit to a Sony factory service center. good Luck

to open them completely simply push them with your finger. try doing so also when closing them. i have the same issue sometimes.

To save battery power, the camera automatically goes into sleep mode and the monitor turns off if there is no operation when the camera is turned on (when the lens cover opens and the monitor is on). No picture is taken even if the shutter button is fully pressed in this mode.
Operate the zoom lever or other buttons to restore the camera from sleep mode before taking a picture. If the camera is left for 15 minutes, it automatically turns off (the lens cover closes and the monitor turns off). Press POWER to turn the camera on.

Same problem. The lens is stuck in the zoom position. When the camera is turned on, the lens moves a just afraction like it want to fully open or close, then the camera beeps and prompts with the "Lens Error" Restart Camera. Solutions?

Try removing the battery for a couple of seconds then insert it again. Click on the power button, it should turn on and turn it off again to close the lens.

The lens cover of PSA60 opens along with the move of the objective lens. Normally the camera will sound an error beep when the lens does not end to the end position -- the lens cover is also not fully opened. In reverse, the lens will be retracted when the camera is switched off.
The "shutter" (outside lens cover) might have something stuck inside the blades or other mechanical parts that prevents the lens cover fully closed. Try to blow with a clean air (no hot air - because it can damage the electronics or plastics).
Or maybe the blades are probably not flat that may create resistance on the surface. Try to flatten the blades by hands.
Or maybe the mechanical systems need to be calibrated (by Canon service center).
My suggestion, try to exchange/trade-in your PSA60 with the latest model at the Canon center, because I have done it last year (trade-in with PS S5IS).

You may have the same problem that i had. It does involve taking the camera apart. Not overly difficult - just fiddly.
Let me know and i'll talk you thro' it

I know this is an old post, but for those who want to fix it themselves: try blowing lots of compressed air around the open lens shutter to clean the mechanism. Or use a hair dryer for a few seconds (don't want to heat up the camera). Also with the lens barrel extended and pointed downward, tap the lens barrel with a pencil while you extend and retract the lens by powering the camera on and off. A grain of sand in the mechanism is usually the culprit, and you want to try to dislodge it.

You can open it up, but only as a very last resort. The above procedures usually work if you try them enough. But for those particularly nasty stuck mechanisms, here's an example repair on a Canon Powershot A400 (do this at your own risk):

http://camerarepair.blogspot.com/2007/11/repair-of-stuck-lens-covers.html

Here's a fix for a Canon A400 lens cover. See if it's applicable for you:
http://camerarepair.blogspot.com/2007/11/repair-of-stuck-lens-covers.html