Mac – Input/output error using Mac Disk Utility

Disc might be spoilt or faulty most probably. Clean the disc, enable any error-correction on your image conversion software, and give it a go again.

I would first start by doing the easiest thing, and storing the exact byte-for-byte copy of the discs on your hard drive in .ISO format. There are various software tools that can do this for you, although you will want to find software that can handle any read errors gracefully.

Personally, I would archive all of the media using the H.264 codec, and store the files in .MKV containers. This will allow you to store the DVDs at very high quality, while maintaining a decent file size. Furthermore, the .MKV container allows for you to setup chapters in the video stream, and you can also find tools to convert DVD chapter formats to the MKV-style chapters.

When ripping the video, doesn't this introduce additional errors (because of the decoding/encoding)?

It depends on the condition of the storage media, and what you do with the files afterwards. Most commonly, you might find a few bit errors in the source media. These can be ignored, at the expense of visual artifacts.

You could try to overcome this with software tools that support attempts to read bad sectors off of the media, but in most cases, there's not much you can do except ignore the error (it shouldn't make a huge difference when dealing with video streams). If the actual MPEG transport stream itself has been corrupted, there are software tools to rebuild/fix the stream headers.

You will also incur a slight loss in quality if you choose to re-encode the stream, although this is arguably negligible depending on the codec, encoder quality, number of passes, and bit-rate. If selected appropriately, this should not visually or audibly affect the video stream in any way.