I have this same printer, though mine is grey and black where as I notice the one in the picture is white so perhaps over time changes have been made to rectify some or all of the issues mentioned. It was available fairly cheaply for around £40 at a clearance so as a result two of my family members bought them as well as have experienced the exact same problems.
The item includes a standard inkjet printer, a black/white or colour copier for which the computer isn't required and a scanner. This is good considering that the whole thing takes up little more space than a standard inkjet printer alone. The printer takes 21/22 ink which can be bought very cheaply now which makes the printer all round good value in terms of cost. You don't receive a printer cable with it, so one of these is required to be bought separately but these can be very cheap.
There is one huge problem with it however, which both myself and relatives who bought it encountered which is that it doesn't function well at all on Windows Vista (it is listed as being Vista compatible). First time installation is slow but steady and everything goes as it should. The printer will work fine until it is switched off, as when it is next turned back on it will be recognised as new hardware and Vista will go through it's usual 'new hardware' installation. Eventually, you will then be brought to the HP installation screen where you then have to find and insert the disc you used to originally install it and wait a little while. Then, when this is all over you can finally print. The printer will now be appeared 'Printer (Copy 1)' or however many times you have had to repeat the process. The 'copies' all build up which makes things very confusing so you have to occasionally uninstall it and then re-install, which takes a very, very long time. Additionally, if you haven't gone through the tedious steps to 'add' it again, the scanner will not work either.
At times, you will be using the computer for internet browsing, typing or anything else that has nothing to do with the printer, when a message will popup in the bottom right hand corner accompanied by a loud "ploop" sound to draw your attention. I haven't failed to get a fright from it yet, and it's only asking you if you want to update or not. Sometimes I click that I do want to update in hopes they will have ended the Vista problem which they never have, other times it starts itself updating in the middle of what you are doing anyway.
It is a good printer as it is, very good, but with the compatibility issue, I hate knowing that I need to use it as I know I will have to go through the same endless procedure each and every time so try to avoid it, and when I can afford to get a new one - I will!