As you haven't provided an aural tests I can't tell how bad your problems but I will still try to help anyway.
Call Volume.
Try setting the equaliser to 'Bright' this should help with the loudness and clarity of the speaker when in a call.
Speaker Volume.
Activate Clear Phase and xLOUD under Sound in the settings menu. This should provide you with a small boost to your overall volume capabilities.
Users have complained that even with these functions enabled that the sound isn't loud enough, this could be restricted by the software to prevent hearing damage as new laws recently have been put in place restricting the volume of devices such as mobile phones, whether the Z has been affected, I am not sure.
If you phone gets wet and the speaker is submerged and or gets water inside, the volume will reduce significantly till it has time to dry out. The best way to do this is to simply blow into the speaker after retrieving it from the water/situation and then leaving it in a warm, dry place to dry out suffeciently. Using the speaker while it's trying to dry out will cause the drying process to take longer.
Heating.
This phone is tightly assembled meaning that the parts are very close in proximity to one another. With high end hardware such as the quad core processor unit in the Z, it is going to heat up. Especially when playing games or using the screen to watch movies ie anything graphics intensive will cause the phone to heat up. The feeling of this heat will be exacerabted by the size of the phone and how it is put together. Software comes pre-installed on the Z to prevent any overheating issues so you do have some peace of mind your phone will not burn out. Because this phone is equipped with a processor such as this one, it is bound to heat up, its expected and there is nothing to worry. Using wifi and data connection will also heat up the device if your constantly connected, be wary of this but still know that your phone can and will get hot but its still safe.
That being said, if you believe it's getting too hot, more than it should be. A hardware fault may be present and taking it back to the SONY store or a repair centre is your only option.
I hope I could be of help to you.
