Apart from bandwidth selections and passband tuning, the IC-7000 has a nice selection of tools to fight the noise and splatter that's left. There is often a lot of it, especially if you fancy MW stations from outside your own continent.
The Noise Blanker is as far as I can see a traditional tool that should cope with ignition noise and similar pulse-type noise. It is adjustable. I haven't had the chance to test its capabilities yet. Reason: Absence of pulse-type noise.
The Noise Reduction is adjustable as well, and a modest level of NR (2-4 out of 10) actually increases the S/N ratio of the station by a couple of dB. In some cases the difference between readable and not readable. The function works more or less the same way as in the 746Pro and is a useful tool.
The Auto Notch Function deals effectively with hets, up to three tones at a time, and it tracks the tones when tuning (or if the tones move).
The Manual Notch Function can be set to attenuate a frequency. Actually there are two manual notch filters, each can be tuned to the desired frequency and they can be individually set to Wide, Medium or Narrow filter width. There is no advice on how many Hz the selected filter width is.
I will dwell a little with the MNF because I discovered that it is in fact a wonderful tool. I was listening to a noise-ridden Radio America, Paraguay on 1480 (LSB to avoid the DRM hiss on 1485, hence subject to splatter from 1476), when I more or less by chance turned on the MNF function. Splatter almost gone!! And I hadn't even tried to tune the MNF filters! Now, what was going on here... I tuned a 746Pro to 1480 and tried to engage its (single) MNF to reproduce the effect. No way... Apparently, the MNF, especially when set to "Wide" filter width, is capable of reducing the effects of splatter with a significant amount, resulting in a noticeable (I was about to use the word "dramatic" but I'll hold my breath) improvement in the signal's readability. I have a couple of recordings which I can email to anyone interested. DRM hiss was also reduced significantly, but I have yet to find out if it means that stations can be dug out of the noise. Effective use of the MNF may require some training.
Audio quality will suffer from the tools listed above. Not much really, actually very little but if you put all of them into use simultaneously audio quality will degrade so much you would probably be better off in the first place.