The LED in the mute key doesn't work out of the box. To enable it, add a file /etc/modprobe.d/hp-spectre.conf with the following contents:

To get an idea about the current status of your batteries, there are a few apps available:

The original firmware in the HP 50g emulates a Saturn CPU like the HP 48 and HP 49 had. However, the built-in ARM920T processor has more power than the Saturn.

The default key debouncing wait time in the HP 50g is very long so that it misses lots of keypresses when typing fast. E.g. when typing 500 the calculator only registers 50. This behaviour is controlled by the KEYTIME setting.

BIOS updates are actually done via the hidden HP_TOOLS service partition which you can get to by pressing F2 after switching on the notebook or from the Startup Menu. The update you download from the hp service page merely copies the new BIOS files to that partition.

Endless feeding