Where does God dwell?
1 Kings 8:13 I have surely built thee an house to dwell in, a settled place for thee to abide in for ever. (cf. 2 Chr. 6:2)
Acts 7:48 Howbeit the most High dwelleth not in temples made with hands...

Technically there is no formal contradiction here of the sort that could worry an inerrantist, since 1 Kings just reports what Solomon said, and he obviously need not have been perfect. But as it happens the word for "dwell" is very rare in the OT, used only five time -- twice in the passages noted above, and elsewhere:

Ps. 49:14 Like sheep they are laid in the grave; death shall feed on them; and the upright shall have dominion over them in the morning; and their beauty shall consume in the grave from their dwelling.
Is. 63:15 Look down from heaven, and behold from the habitation of thy holiness and of thy glory: where is thy zeal and thy strength, the sounding of thy bowels and of thy mercies toward me? are they restrained?
Hab. 3:11 The sun and moon stood still in their habitation: at the light of thine arrows they went, and at the shining of thy glittering spear.

The last cite tells us that the word here simply means "a place where they are" with no connotations of setting up housekeeping (versus the NT word katoikeo, which is used in verses like this: "And he came and dwelt in a city called Nazareth". There is another Hebrew word for this, yashab.)

Correspondingly this would simply refer to a place where a deity could make contact and communicate its will; for the pagans that would have been an image of some sort, but for Yahweh that would be the Temple in Jerusalem.

Objection: It's obvious that the two words 'abide' and 'dwell' are used as synonyms in 1 Kings 8:13. They are used in poetic parallelism.

The fact is that the words are not synonyms, and that they are used in a poetic parallelism does not make them synonyms either. This "answer" merely creates a rule that words used in a poetic-parallel structure are automatically FULL synonyms. They do have related meanings, of course, and that is all that is needed.

Note that "abide in" is paired, by the way, with "for ever" which indicates that it has a different and more permanent connotation. Of course, anyone who wishes to simply list verses with each word will have to do some real work and exegete them.

Solomon says in 1 Kings 8:12 that God said He would 'yashab' forever in the Temple. And David wanted that, too.

And of course, it was obviously David and Solomon's earnest hope that God would set up permanently in the Temple, but where that fails is in that such permanent abiding was contingent upon obedience to the covenant -- but that's not what happened, and his expectation and hope does not equate with the reality, so that by Paul's day it was certainly not in error for him to say that God did not or had not set up permanent shop in any temple.

For Paul, Jerusalem was a city under judgment -- and there was no presence of God in the Temple to speak of, and probably had not been, in his view, since at least the time when the Romans invaded and park themselves in the Temple.

In 1 Samuel, 2 Samuel, etc. it says God 'yashabed' between the cherubim.

Yes, and what? That's not the Temple. It's the Ark of the Covenant. It is a contrivance to say such things as, "the ark is a retrojection of the Temple".

Solomon clearly thought that he was building a 'settled place' for Yahweh to dwell, so until the completion of the temple, Solomon apparently thought that Yahweh's 'settled place' was in heaven but would thereafter be in the temple.

This needs to be informed by the ANE concept of a hypostatic entity. By means of a hypostasis, a deity was able to reside in heaven but also dwell (to whatever extent) on earth.

Matt. 23:21 uses 'katoikonti'. It says, 'Whoso therefore shall swear by the altar, sweareth by it, and by all things thereon. And whoso shall swear by the temple, sweareth by it, and by him that dwelleth [katoikonti] therein.' That shows that Jesus thought God resided in the Temple permanently.

This is where serious historical study again aids the answer. Keep in mind that this was the very Temple that Jesus cleansed as a prophetic demonstration indicating that it was NOT the dwelling place of God, but had been abandoned by God because of the sin of Israel.

With that in mind, Matt. 23:21 -- which is part of an invective against the Pharisees and what they did and believed -- represents nothing more than a case of Jesus granting a premise that the Pharisees accepted (God did dwell in the Temple at that time) in order to denounce them for their behavior in using the Temple as a swearing device.