(1) Paul says a Justification took place in the prayer David made when composing Psalm 32. Since David is not converting to Judaism at that time, it can only mean he lost his justification through grave sin (adultery and murder) and was repenting to become Justified again. In fact Luther himself taught David lost his salvation: “[W]hen holy men, still having and feeling original sin, also daily repenting of and striving with it, happen to fall into manifest sins, as David into adultery, murder, and blasphemy, that then faith and the Holy Ghost has departed from them” (Smalcald Articles #43). This irrefutably contradicts the Calvinist idea that Justification cannot be lost.
(2) The text of Ps 32:2b says “in who’s spirit there is no deceit,” which means an inner sanctification took place at that moment as well. Some might object that Paul didn't quote the rest of Psalm 32, including this stanza, and thus he didn't mean to include 32b in his lesson in Romans 4. But if that is true, it means Paul selectively quoted David out of context (which nobody believes). This conforms to David’s description of being forgiven elsewhere, such as being “upright of heart” (32:11) and “wash me thoroughly from my iniquity, and cleanse me from my sin … purge me with hyssop, and I shall be clean: wash me, and I shall be whiter than snow.” (51:2,7). It is plain that Psalm 32 and 51 go together, especially since there cannot be two forms of God's forgiveness. This description of what Justification entails, namely an inner sanctification of the soul, is precisely what Catholics teach but completely unacceptable for Calvinists because they think it would be conflating Justification and Sanctification (though Paul never makes this distinction that Calvinists teach).
(3) When David says “blessed is the man against whom the Lord will not reckon his sin,” this can only mean God will not reckon him a sinner because his sins have been forgiven, as the context clearly speaks of forgiveness (32:1). The term “reckon” here puts the Calvinist in another serious bind, since it’s the same Greek term Paul uses throughout the chapter when speaking of “reckoning righteousness”. The Greek term (logizomai) cannot mean “to transfer,” since it would then mean “Blessed is the man whom God will NOT transfer his sin” – and thus the term “reckon” can only mean to ‘evaluate as’. This means that when Paul speaks of faith being “reckoned as righteousness” (in the very same context), he cannot be speaking of transferring an alien righteousness, but rather must mean ‘evaluating faith itself as having a righteous quality’.
(4) In Romans 4:6-8, Paul equates the phrase “reckoning righteousness” with David's phrase of “not reckoning sin”. In other words, rather than being two different reckonings, they are one and the same, simply from two different perspectives. For example, if I clean a stain off my shirt, I can just as easily "reckon cleanliness" to my shirt as I can "not reckon a stain" on it, since both phrases refer to the same reality. This realization is huge and explicitly refutes the Calvinist notion of double-imputation, where not reckoning sin (i.e. forgiving) is seen as one half of the equation, bringing the sinner from a "-1" to a "0" state, and reckoning righteousness (i.e. transferring a perfect obedience to God's law to his record) is seen as the other 'half' of Justification, bringing the sinner the rest of the way from a "0" to a "+1" state. Given Paul's equating of the two, it’s impossible to say “reckon righteousness” is one half of the picture and “not reckon sin” is the other half, since they are synonyms here. To buttress this point, Luther and Calvin made this same claim, namely that Paul is teaching the two phrases are synonymous, which is also why they didn’t believe in the Active Obedience of Christ.