I've had the x10 mini since feb this year.
If you are after a small phone you will not get one smaller!
The screen is okay, but in sunlight it's absolutely useless, even with the brightness turned up (then I suppose what smart phone isn't the same?). So you need some shade if using the phone outdoors on a sunny day. (I work outdoors so this is a big thing for me).
App market seems to work fine with such a small screen. The text is small but not small enough as to not be able to read it.
I never use it online (apart from wifi to look at the android store occasionally) but it has facebook, google maps, gps etc (although I haven't used them). Gingerbread 2.3 update is due for this phone in the last quarter of this year 2011, not sure if skype is included with that though.
I intend on keeping this phone either until it dies on me, or a better, smaller/same size, phone surfaces which doesn't look likely at the moment.
other small gripes are (which may probably just me but) occasionally the screen will default to standby (switch off) after 3-5 seconds when you are using it, which can be annoying. Pressing the screen (with multitap on) can sometimes skip ahead more than you want it to, so text messaging takes longer. Battery time really sucks if you use it a lot, I found it's best to not use an app killer (as so many suggest) and to turn the phone off when it's not in use (that has doubled the charge longevity for me), although if you're the type to have your phone 'always on' the battery life will annoy you pretty soon, and the battery is not easily removed, you have to dismantle the phone in part to get to it (the cost of having the smallest android I guess!).
other than those small annoyances I would recommend it (oh' and the camera is very good on this ericcson, so another + there!). if in doubt you can get them on ebay for around £40-50 now, you could always buy one there, test it and then sell it on if you're not happy with it.