DEADn,
Very good question. A lot of unbelievers and heretical teachers throw this in our face in order to cause us to stumble.
The way I approach Scripture is with the assumption that it is infallible. There are a great many variants within texts that we use for Bible translation. I actually am of the thought that anything that appears to be added is actual, and anything that appears to be missing is--well--missing.
A man would have to consciously make up stuff in order for it to end up in the scripture. It was not common to thrust in commentary or side notes into the middle of the text, so that is unlikely to have occurred, although not impossible.
It is actually much easier for a man to drop out a line of text while copying or drop out a word.
And I believe these types of errors are easily reconcilable.
Let's look at the whole text with and without the passage in question:
Here it is without the text:
5 After this there was a feast of the Jews, and Jesus went up to Jerusalem.
2 Now there is in Jerusalem by the Sheep Gate a pool, in Aramaic[a] called Bethesda,[b] which has five roofed colonnades. 3 In these lay a multitude of invalids””blind, lame, and paralyzed.[c] 5 One man was there who had been an invalid for thirty-eight years. 6 When Jesus saw him lying there and knew that he had already been there a long time, he said to him, "Do you want to be healed?” 7 The sick man answered him, "Sir, I have no one to put me into the pool when the water is stirred up, and while I am going another steps down before me.” 8 Jesus said to him, "Get up, take up your bed, and walk.” 9 And at once the man was healed, and he took up his bed and walked.
Here it is with the text:
5 After this there was a feast of the Jews, and Jesus went up to Jerusalem.
2 Now there is in Jerusalem by the Sheep Gate a pool, in Aramaic[a] called Bethesda,[b] which has five roofed colonnades. 3 In these lay a multitude of invalids””blind, lame, and paralyzed waiting for the moving of the water; 4for an angel of the Lord went down at certain seasons into the pool, and stirred the water: whoever stepped in first after the stirring of the water was healed of whatever disease he had.[c] 5 One man was there who had been an invalid for thirty-eight years. 6 When Jesus saw him lying there and knew that he had already been there a long time, he said to him, "Do you want to be healed?” 7 The sick man answered him, "Sir, I have no one to put me into the pool when the water is stirred up, and while I am going another steps down before me.” 8 Jesus said to him, "Get up, take up your bed, and walk.” 9 And at once the man was healed, and he took up his bed and walked.
So, there are plenty of arguments about why it should not be included; however, one of the best things you can do with these is see how the context acts with and without it.
Without that variant text, I am left scratching my head, saying, "What on earth does verse 7 mean????" With that variant text, I understand fully what the situation is. And that is important.
The question then becomes did an angel really do that? Well, I tend to lean toward a face-value reading of scripture. So yeah, an angel could have done that.
One of the things that I notice about passages that are in question is that they are NEVER PC passages. There is usually some hot-button issue being discussed in them. Your John 8 passage is very similar. Jesus let a woman guilty of adultery go! That is CRAAAZY!
Do I believe it happened? Yes.
In 1 John, we know the Trinitarian passage. I am a big fan that it should remain in the text.
That's how I kind of go about dealing with this.