Fortunately, there are a lot of utilities in Cydia (accessible from any jailbroken iDevice) that provide help in using these devices.
Generally, they're easy to use: get the apps from Cydia. The mouse handler (BTstack
All these apps put an icon on the SpringBoard. Whenever you want to connect and use the hardware, you tap the icon, initiate connection by selecting the device from the list and that's all.
Let me present you an example of such a list. This is the main device selector list of BTstack Keyboard (as usual, click the thumbnail image for the original, large, high-quality version!):

BTstack GPS 1.5-25900
This has nothing to do with the well-known GPSed service
Also note that there aren't apps that would make a iPad (2) 3G or non-first-gen iPhone (these models are all GPS-enabled) a real Bluetooth GPS source. THIS page lists some of the currently available, GPS-related Cydia apps; in addition, THIS
Finally, note that xGPS is also available in Cydia. It's the poor man's Navigon / iGo Primo / Sygic / you-name-it. It, among other things, allows for downloading the full Google maps of an area for strictly offline (no roaming data fees etc., unlike with the built-in Google Maps) navigation. It's, however, incomparably worse than any of the above-mentioned titles (no POI's, crashes easily, no Retina support with maps etc.) Better wait for a price drop of the “real” maps – in general, once a year or two years this does happen. (Actually, it was during such price drops than I purchased mine; for example, both Navigon's and Sygic titles were heavily (50% off) discounted in Aug 2010 (e.g., 45 / 20 euros for the full European / US maps, respectively) and April 2011 (13 euros for the Central-European maps), respectively.) It, however, can log your track, which, later, can be used to tag your photos taken with a separate, non-GPS-enabled stills camera. I may elaborate on this in a later article, with particular attention to dynamically(!) geotagging videos, which may not be supported by recent desktop software titles, unlike, say, the Panasonic pocket superzooms TZ-10/20
A dedicated, highly recommended article is HERE
BTstack Keyboard by Matthias Ringwald 1.0-25570
While most Bluetooth keyboards (e.g., Apple's own Wireless Keyboard
Interestingly, under OS5, the operating system message has changed a bit. This is how it looks under iOS versions prior to iOS5:


Needless to say, the message used in iOS versions prior to iOS5 is more straightforward as casual iOS users will know right away their hardware isn't supported. The new error message is pretty confusing and will result in a lot of poor users' trying to reconnect, re-power their keyboards. Apple might want to re-introduce the old message to avoid user confusion.
The Keyboard app does wonders and works just great together with my first-gen Apple keyboard. Of course, it isn't as seamless as using a standard one, but I've decided not to upgrade my (otherwise, really rarely-used) keyboard until Apple releases one with backlighting.
I've tested this all with the Mogo PCMCIA-shaped mouse; it worked just fine. Note that it's stated to be incompatible with the Apple Magic Mouse (I haven't tested this). With previous-generation Apple mice like the one-button Wireless Mouse it does work for about 30 seconds and, then, in the majority of cases, it just shuts down. I've tested this; the same mouse works with OS X just fine; that is, it's working with the desktop flawlessly.
If the mouse is auto-discoverable (the case of, among others, the above-mentioned, albeit incompatible [see the disconnection after half a minute] Apple Wireless Mouse), at least making it is not necessary.
Using both the mouse and keyboard at the same time
If you connect your mouse first and try to connect the keyboard after this, it won't work. Fortunately, you don't need to wait much to find it out: if, instead of the keyboard icon (or, for that matter, mouse icon when trying to connect your mouse), all you see is a blue, generic Bluetooth icon on the left, connecting just won't succeed. A screenshot of this:

I, on the other hand, had no problems with connecting the keyboard first and, then, the mouse. You may also want to go this way.
Please also see the third (and longest) video on the parallel usage of the keyboard and the mouse and the order they need to be connected.
Remember my article “Zeemote - right now, the best Bluetooth game controller - on WinMo / iPhone soon?”
It's nearly not as good to play as a BT mouse in, say, Battle Squadron 1 and can't be used with any game with a D-pad as it's, essentially, a joystick-based emulation of a mouse cursor. If you've ever done it on any platform (e.g., moving the mouse cursor on the PC's keyboard), you know how hard it is. As there's not any iDevice app in the appstore to take advantage of the Zeemote, currently I don't see much point in using it. Unless you absolutely don't have access to a Bluetooth mouse but do have a Zeemote and want to move the pointer around / remotely suspend/resume the device / start and exit apps.
The driver doesn't work together with the other human input drivers (so that, for example, you can “press” the Home / Power buttons from afar). If you start it with the other two active, it won't connect. If you connect it first to your Zeemote controller and only after that to your mouse, the Zeemote connection won't live long.
ZodTTD's emulators don't support the pad either, and it's highly unlikely they ever will as ZodTTD (as with the developers / porters of the PSX emulator, FPSce) seem to have completely switched to Android because of its far more game console emulator developer-friendly approach.
iOS5 compliance
I've prepared three videos showing BTstack Mouse / Keyboard
Let's take a look at the second video, which demonstrates the disconnection problems of the Apple Wireless Mouse. These problems surface at 0:48 and 1:46; in both cases about 30 seconds after establishing the connection. As you can see, the mouse, in this state, is useless. (Albeit, for some reason, sometimes it doesn't disconnect...)
The video (original HERE):
Now, the third video shows a lot more; for example,
a.) connecting the Mogo mouse and playing Battle Squadron 1
b.) using the Mogo mouse and the Apple Wireless Keyboard at the same time, including the right order of connecting (remember: keyboard first, mouse second). I also show how you can quickly notice you've used the wrong order (or there's another problem) as, after finishing playing, I don't disconnect the mouse but try to connect the keyboard right away. (This happens from 3:33; it's at 3:49 that I switch on the keyboard; in a second or two, it becomes visible to the iPad too.) Notice the blue, generic Bluetooth icons on the left! This means it won't connect. This is why I first respring the device and when I, at 4:13, realize keyboards will still not work, I respring again. This time, I also shut down the “Keyboard” app (at 4:19) so that it can re-discover the Bluetooth devices.
After the second respringing, the Keyboard app started working (it's impossible to tell how many resprings you're going to need) and I could enter some stuff to Notes (at around 5:10). After this, in order to show both the correct order of co-using the mouse and the keyboard, I start connecting to the mouse with the mouse app. (Note that, again, I had to make the mouse discoverable so that BTstack Mouse sees it at around 5:22.) After this, at around 5:40, I show how the two input peripherals can be used together.
The video (direct link):