What are examples of these type of problems? Well, for example, there are already autonomous lawnmowers that will wander around gardens all afternoon. The next step might be autonomous vacuum cleaners inside the house (though clutter and stairs present immediate problems for wheeled robots). These are all sorts of other uses for artificial animals in areas where people find jobs dangerous or tedious - land-mine clearance, toxic waste clearance, farming, mining, demolition, finding objects and robotic exploration, for example. Any jobs done currently or traditionally by animals would be a focus. We are familiar already from the Mars Pathfinder and other examples that we can send autonomous robots not only to inhospitable places, but also send them there on cheap one-way `suicide' missions. (Of course, no machine ever `dies', since we can restore its mind in a new body on earth after the mission.)
Whether these type of machines may have a future in the home is an interesting question. If it ever happens, I think it will be because the robot is treated as a kind of pet, so that a machine roaming the house is regarded as cute rather than creepy. Machines that learn tend to develop an individual, unrepeatable character which humans can find quite attractive. There are already a few games in software - such as the Windows-based game Creatures, and the little Tamagotchi toys - whose personalities people can get very attached to. A major part of the appeal is the unique, fragile and unrepeatable nature of the software beings you interact with. If your Creature dies, you may never be able to raise another one like it again. Machines in the future will be similar, and the family robot will after a few years be, like a pet, literally irreplaceable.
What will hold things up? There are many things that could hold up progress but hardware is the one that is staring us in the face at the moment. Nobody is going to buy a robotic vacuum cleaner that costs £5000 no matter how many big cute eyes are painted on it or even if it has a voice that says, "I love you". Many conceptual breakthroughs will be needed to create artificial animals. The major theoretical issue to be solved is probably representation: what is language and how do we classify the world. We say `That's a table' and so on for different objects, but what does an insect do, what is going on in an insect's head when it distinguishes objects in the world, what information is being passed around inside, what kind of data structures are they using. Each robot will have to learn an internal language customized for its sensorimotor system and the particular environmental niche in which it finds itself. It will have to learn this internal language on its own, since any representations we attempt to impose on it, coming from a different sensorimotor world, will probably not work.