Is the /P/ often missing from the start of words? I'm hearing this from some of the audio samples.
It's not missing, at least not in this recording.
Are you a native English speaker? There are two things different here:
English aspirates word-initial P, T and K (adds a small H sound after them), and Polish doesn't. You expect that H and it's not there, so you think something is misssing.
some dialects of English usually pronounce P with more strength than B (fortis vs lenis), while in Polish those sounds don't differ in strength. A weaker Polish P may appear to you as too weak.
Oh so the p isn't aspirated? Good to know! All right, I'll have a good listen out for these. ^^