The one thing I see the most go wrong with people applying for Government jobs, is they don't know the lingo. With the internet, preparing for a Government Job is easier than in the past. Look at your job announcement, then look at other sites and forums which highlight this job. Learn the names of the regulations you will be following and read a little in them.
Ok so you are a lead in Program Management, but do you know the financial regulations, and program management regulations you will be following in that position? Do you know the lingo in Program Management in the Government?
Details, details, details and use the keywords. Some people don’t like the way the Government hires, but as long as they are still doing it this way, do it the way they want, and you will eventually get hired.
Don't be afraid to bring in all your certificates and training from your prior positions and TAB them with flags with Government Keywords. You may have received a training certificate in so-in-so at your last job, but you know it fits in perfectly with a particular keyword you see in your application. Tab the thing and hand it to the panel when they ask a question.
Government people have no reason to fear you stealing their jobs (at least not right away), so they are not going to NOT HIRE you for looking too good. This is your moment to shine. They are not the enemy. Show the panel in many ways how your civilian jobs transfer to your new Government one.
This is going to sound over the top - but it worked. I helped someone get a Government job once by doing this...
All she had was all civilian stuff, so we made a three ringed binder of everything she had and divided it into sections; career training, formal higher education, and awards. Then we put sticky notes on each one of them with notes showing where each one fit in with the Government job (using key words from the announcement). She gave the binder to the board, and BAM she was hired. Just like that!
*** Keep in mind, we also used the same notes and keywords in her resume. I know KSAs are controversial, but make the most out of them. Every single question on the resume gives you one more time to highlight how great you are. Don’t waste it by being lazy.
On the other hand, I am working with someone right now who does not want to seem egotistical by providing too much information. They are taking a huge risk. You get one time in front of the board. Take the time to shine.