Matthew 21:16 follows the Septuagint's 'perfected praise,' but the Masoretic has 'ordained strength'; which is right, and does it affect inerrancy?

No, it does not affect inerrancy, because the Septuagint is not inspired; it is a translation and prone to error. First you have to make sure the Masoretic text is right, since it too can have occasional problems, and then remember the Septuagint is only a translation. Paul used the Septuagint often, but that is because the people had been using it for three centuries, not because it was perfect; the Alexandrian Jews used the Septuagint and the Palestinian Jews used a Masoretic-type text. And Paul sometimes had theological reasons to quote one or the other, or neither: in Romans 11:26 he writes 'the deliverer will come from Zion,' whereas Isaiah 59:20 says 'to Zion,' so Paul changed the preposition to a third option to make his own point. My first inclination here would be that the Masoretic text is the one to choose, unless there is a good reason the Septuagint changed it, because the Hebrew is sometimes more flexible than we allow; the vowels were not inspired, and if you get a vowel wrong you can get the word wrong and throw off the whole sentence. In my commentary my footnote on Matthew 21:16 deals with the point that Jesus applies the psalm to Himself, which to the chief priests' dismay means He is the very God the boys are praising, but it does not settle the textual question directly.