By mistake, I booked my flight using initials for my first and middle names. On my id, both names are written in full; the last name is the same. Can I travel on a domestic flight with this mistake?
In some cases the airlines will not have any problem with the difference, in other cases they will not accept it.
As soon as you notice the problem you should contact the airline you have bought the ticket for and ask them whether you need to do something and how to do so.
In some cases it is not the airline but the airport who might stop you from going to your plane, in that case having contacted the airline (and gotten a correction if needed) you can show the airport security officer that you have done what is needed. They should let you go on then but if you get any paperwork or an e-mail (or alike) answer, bring it.