Batteries.
Here are a few notes I have put together about batteries.
Whether you use regular or rechargeable batteries you should buy the best. Discounted or unbranded batteries are more likely to give a poor performance and may be of irregular size ... which all too often will lead to connection problems.
It is my experience that Duracell 2400, Eneloop and Energiser are the best. Apple batteries of late do not always perform well, rarely exceeding seven to nine days before a need for recharge. But the Apple charging unit is excellent and comes with 6 batteries which means you can always have 2 charged and ready.
Rechargeable batteries for a Magic mouse are unlikely to exceed sixteen days before needing recharge although the brand of mouse can be important; I have seen reports that some Logitech mice vastly exceed this. Apple may suggest more in their sales blurb but this is a realistic expectation. Regular batteries will give you between 25 and 35 days before they need to be replaced. Green aspect apart, the main benefit with rechargeable batteries is that you can always have batteries on hand that at worst need only a top up.
Note(1) Never mix old and new batteries or rechargeable and regular.
Note (2) Monitors do not always faithfully report battery strength, particularly the rechargeable ones.
The notes above are based on my personal experience, not shutting down my machine and using it for around four hours per day.
When checking your mouse or keyboard batteries ... Turn off the device. Remove the batteries, Clean the terminals both inside the battery compartment and those of the batteries themselves. Replace both batteries or renew them if necessary. Turn on the device. You should get a blinking green light if the device is paired. Click the mouse to activate it. The green light becomes steady.
Many people find problems with opening the Magic Mouse 1 battery compartment. Here is what to do.
Hold the mouse upside down, green light indicator to the top. Turn off the mouse. Open the battery compartment by gently flicking the black rectangular button at the bottom in a downwards direction; I find the middle finger best. It can be a delicate operation and you may need to do this two or three times before the compartment plate will come away, allowing you to remove the batteries.
After the batteries have been charged or replaced, press the top section in first then apply light pressure to the bottom section so that the plate clips over the black rectangle. Turn on the mouse, click twice and you should see a steady green light.