4... Is there stuff missing from modern translations?

Table of contents:

A... It's about manuscripts, not translations.

You can't tell how a verse should be translated by comparing translations.
All that tells you is how it was translated.

You must look at the manuscripts if you want to know how a verse should be translated.

A manuscript is a handwritten copy of a portion of scripture.
We don't have the originals any longer; all we have are copies.

The KJV isn't a good translation because it came first and has more words.
The KJV is a good translation because it is faithful to the manuscripts that the KJV translators had available to them.

Modern translations aren't bad because they disagree with the KJV.
Modern translations are good because they are faithful to the manuscripts that we have available today.

B... Almost all modern translations use different manuscripts than the ones that the KJV is based on.

The differences that you see when comparing KJV verses to verses in modern translations are because we use different manuscripts today than the KJV translators used.

There were 25 manuscripts used for the KJV.
Today we have over 5,800 Greek New Testament manuscripts.
They were not written since the KJV was translated; rather, they were discovered since the KJV was translated.
The KJV textual critics and translators did an amazing job with what they had.
They used all the manuscripts they had available to them.
Today, we can pick and choose the best manuscripts.

C... All manuscripts have mostly tiny differences or errors called textual variants.

"If you put ten people in a room and asked them all to copy the first five chapters of John’s gospel, you would end up with ten different copies of John. In other words, no two handwritten copies would be absolutely identical to each other. Someone would skip a word that everyone else has. One person would misspell that one word they can never get right. Someone would probably skip a line, or even a verse, especially if there were similar words at the beginning or end of the verse before and the verse after. So you would end up with many variants. But would you not have ten copies of the same book? Yes, and by comparing all ten copies you could easily reproduce the text of the original, because when one person makes a mistake, the other nine are not likely to do so at the very same spot."

...from The King James Only Controversy, 2nd edition, 2009, p. 277

Handwritten copies almost always contain errors.
The invention of the printing press greatly reduced errors.

Manuscripts have tiny differences called textual variants.

The Bible is providentially preserved, but it takes some work to determine the exact original reading from the copies.
Sometimes the exact original reading can't be determined.
There may be two or three possible readings.
Textual criticism is the science of comparing manuscripts in order to determine the original reading.

So, textual variants are the main reason behind the differences between the KJV and modern translations.

D... Less than 1% of all the textual variants significantly affect the meaning of the overall Bible.

A few textual variants are very dramatic, like Mark 16:9-20 and John 7:53-8:11.
But most textual variants are so minor they can't even be translated.
For whatever reason, God did not choose to preserve the Bible exactly word-for-word from one manuscript to the next.

According to https://www.str.org/articles/textual-variants-it%E2%80%99s-the-nature-not-the-number-that-matters, less than 1% of all textual variants are viable and meaningful. Viable means the textual variant could have been in the original text. Meaningful means the textual variant changes the meaning of the text.

"A quantitative study on the stability of the New Testament compared early manuscripts to later manuscripts, up to the Middle Ages, with the Byzantine manuscripts, and concluded that the text had more than 90% stability over this time period.[117] It has been estimated that only 0.1% to 0.2% of the New Testament variants impact the meaning of the texts in any significant fashion.[117]"

...from https://en.wikipedia.org/wiki/Historical_reliability_of_the_Gospels#Texts

Parallel verses:

There's a lot of repetition in the Bible.
Many of the "missing" verses resulting from textual variants have parallel verses.

More info here

Are there mistakes in the Bible?

The short answer is, "No.".

Our English bibles probably don't contain errors...

That's the point of textual criticism--
...to identify errors in the manuscripts and correct them in the translation.

God's revelation and the original autographs are / were without error.
Variant readings resulting from scribes' errors do not mean God's revelation is in error.

Wikipedia - major textual variants in the New Testament

Here is another website which lists textual variants.

So, the manuscripts contain mistakes, but they make very little difference.

E... There isn't stuff missing from modern translations...
...Instead there was stuff added or interpolated to the manuscripts that the KJV is based on.

Here is the best explanation of this that I've found.

What kind of mistakes did scribes make?

Errors of addition and retention were more common than errors of deletion.

"Two common considerations have the Latin names lectio brevior (shorter reading) and lectio difficilior (more difficult reading). The first is the general observation that scribes tended to add words, for clarification or out of habit, more often than they removed them. The second, lectio difficilior potior (the harder reading is stronger), recognizes the tendency for harmonization--resolving apparent inconsistencies in the text. Applying this principle leads to taking the more difficult (unharmonized) reading as being more likely to be the original. Such cases also include scribes simplifying and smoothing texts they did not fully understand."

...from https://en.wikipedia.org/wiki/Textual_criticism#Internal_evidence

"Dr. Kurt Aland has pointed out what he calls the tenacity of the New Testament text. That is, once a variant reading appears in a manuscript, it doesn’t simply go away. It gets copied and ends up in other manuscripts. Why is this important? Because readings don’t just “disappear” in the New Testament. And this means we still have the original readings of the New Testament works. You see, if readings could disappear without a trace, we would have to face the fact that the original reading may have fallen through the cracks as well. But the tenacity of the New Testament text, while forcing us to deal with textual variants, also provides the assurance that our work is not in vain. One of those variant readings is indeed the original. We are called to invest our energies in discovering which one it is."

...from The King James Only Controversy, 2nd edition, 2009, p. 78