The other answers largely deal with the structural aspects of iron. But there is another property of iron which is widely used: it's magnetic permeability. If you wrap a conductor, such as a copper wire, around a chunk of iron, then pass a current through it, the iron atoms will align themselves with the resulting weak magnetic field, thus amplifying it into a much stronger field. This is the basis behind electric motors and generators, and without abundant iron this line of technology will be severely stunted.
It looks like there are some other metals that may provide a similar, but weaker, effect -- such as nickel, manganese, or gadolinium. But most of the magnetic cores we use are based to some degree on iron, whether in pure form, as an alloy, or as a ceramic. Even if you find alternative materials, the fact that they aren't as ubiquitous or efficient as iron means any such technology is likely to be rare and/or expensive.
It is also the basis behind magnetic storage, such as tapes and hard drives. I was going to suggest that such a civilization might jump straight from vinyl records to optical CDs. But then I remembered that microphones and speakers also rely on magnets, so audio systems in general might not be very common (and this is just one example of how common magnetism is).