Sounds like your distortion occured in the analog domain,prior to digital conversion,and may be embeded in the wave form.You would not see this as a clipped top on the wave,but just to be sure,how hot is your output signal on the meters in Audacity?

As AudioFreek pointed out, if the distortion occurred in the pre-converter section of your gain staging - either by overdriving the pre, or overdriving the mic itself, it wouldn't necessarily show up within your wave form as an actual visual clip or "over", because your input signal - distorted as it may be - may have been within the bounds of your DAW's acceptable input db range...

In short, you don't have to be driving your DAW's input meters into the red to get distortion or clipping. You need to be monitoring the signal from the output of the pre itself. This is simple gain staging .. "audio 101" ....And this is where I'm confused:

I even went so far as to use headphones while recording and did pick up on some distortion but I could not figure out why it was happening.

At which point you should have immediately addressed the issue... checked your pre amp levels, or, if there was a pad on the mic itself, you should have looked at engaging it. In short, If you knew there was a problem, in your case, the distortion on the signal...well, I guess I'm at a loss to understand why you wouldn't have investigated the source and fixed the problem at that point as opposed to waiting until the post stage to address the issue ...?

Anyway, as Freek mentioned, unless your distortion is simply occurring as a result of your monitoring output being too hot, or something that isn't a part of the actual recording, there's not much you can do about that distortion if it was printed/recorded that way to the audio file to begin with.

fwiw
-d.

Some programs are better at correcting over gain, than others. But once the microphone or the preamp is overloaded, there really is quite a limit as to how far it can be reconstituted. Audacity is a good but limited piece of software. It does a whole lot but fixing distortion ain't one of its forte's.

It's a real shame when these things happen, especially if they cannot be redone. So then one of the ways to limit overdrive distortion is to actually narrow frequency response. You roll most everything off at 150 Hz and at 5000 Hz. This limiting of the bandwidth still allows for the talking head to be well understood. Frequencies above 5000 Hz frequently include many additional higher harmonic distortion components than it has to do with the fidelity of the microphone and the person. And it's those upper harmonic components that provide for the most audible sounding distortion.

There are other software manufacturers that actually produce not cheap software for use in restoration of older recordings. These algorithmic functions are far more complicated than comprehensive than most. But there is still a limit as to how much audible distortion they can actually reduce.

There is also a possibility that you might be experiencing a disparity of difference between what bit depth and sample rate the recording was actually made at and what it is trying to be played back through. For instance it might be possible that ya recorded at 24-bit, 96 kHz audio that you are attempting to play back at 16 bit, 44.1 kHz? Or 48 kHz? Without doing a proper downconversion to begin with? Some built-in audio cards within computers cannot reproduce 24-bit, 96 kHz digital audio worth a damn if at all. And this is a common error a lot of folks make when they used those miniature solid-state recorders. Where those made default to 44.1 kHz/48 kHz but at 24 bit depth. And your program expects us to a 16 bit depth recording? This can make someone believe that they have made an error in the original recording when there really isn't one. You said the waveform does not appear to have any flat topped clipped audio to it? Yet you indicate distortion within that audio?

So my next question begs the answer of whether you captured this right to the input of a camcorder or some other device? And then how did you transfer that sound into the computer? Was it a direct digital stream capture? Or, was one audio device output plugs into another audio device input, in order to get it into your computer? Are you actually hearing the distortion with earphones on, from the original recorder, headphone output? And are you sure the output level has not been over cranked to your headphones? It's easy to get confused under some of these situations. And perhaps there really isn't anything wrong with that talking head lav microphone track? In fact it's almost impossible to screw that up. However what's done is done and now we need to see if it is salvageable? You might want to upload it to Drop Box and see if anyone here wants to have a go at it? I certainly would give it a quick shot but I'm not guaranteeing anything.

I came from the land of doing NBC-TV network news. Where intelligibility and not high fidelity are really the most important factors. All that's needed for adequate speech interpretation is a frequency response established by the telephone company 100 years ago of 300 Hz-3000 Hz. The Europeans extended that to 4000 Hz. And nothing above those frequencies. With those extreme high and low cuts, audio sounds just like a telephone that was recorded with a $3000 plus German microphone. Changer rolloff point in the low-end to 100 Hz and you have a beautiful sound that will be reminiscent of old time radio broadcasts with RCA ribbon microphones. And where the filtering will help to eliminate the audible artifacts of overload. Other anti-clip programs will roll the leading edges of waveforms off. Click pop and crackle software noise eliminators can also help to reduce distortion artifacts. And all of this for mackintoshes available from Sony Sound Forage for Mac. I think I recently read something about Adobe's Audition also been ported over to Macintosh? Both of these programs already offer highly effective and sophisticated noise reduction and restoration software algorithms. Sometimes audible distortion can be eliminated with a simple de-crackling noise reduction program? Other programs have overload restoration capabilities that can be tried in various ways. None of which will make the audio sound the way it should have sounded to begin with. In fact it's all a horrible compromise. And we are sometimes filtering it down to the point of sounding like a telephone might be more advantageous than trying to restore what cannot be restored? Basically because you want intelligibility more than anything else from a talking head.

I bet you know how to set your levels better today?
Mx. Remy Ann David