Anti-alias filters are devices built into any normal CD player that plays back regular CDs and CD-Rs containing audio recorded at 16-bit/44.1KHz. It cuts off the high frequencies above 20 KHz that are present in the audio.
The average human ear can detect frequencies between 20 Hz to around 21 KHz. People with exceptional hearing (which usually includes younger folks) can hear frequencies from !9 Hz to around 23 KHz.
The 16-bit/44.1 KHz format cannot reproduce freqs above 20 KHz, so the anti- aliasing filter keeps the frequencies in a range that the format can handle.
All this really means to you, is that if you want to be able to record and play back freqs above 20KHz, you have to record them in another format, such as 24-bit/96KHz. This format needs no anti-aliasing filter because of its increased sampling capacity.
DC offset can happen if your electrical power and your equipment don't play nicely with each other. While I don't understand the exact reasons this happens, I do know the problem that it causes. It decreases the headroom of your recording setup. I'm sure you have probably seen the waveforms that your music "makes" when doing waveform editing. (you know, the wierd squiggly lines that show your peaks.) If you have a problem with DC offset, you can see it in the waveform. The little thin line running horizontally straight through the center of your waveform (the "nothing point), will not actually be running down the exact center of your positive and negative waveforms. (positive is the spikes above the line, negative are the spikes below it.) The spikes on one side will therefore be longer than the ones on the other. So you lose headroom and cannot get as hot a signal as you should normally be able to without causing clipping and distortion.
I didn't mean to write a book here, but these are complicated subjects that require just as complicated answers.
Hope this helps.