A few thoughts:
First, his definition of "substance" and "administration" is incorrect. He got the words right, those are two really important words. And he is right (sort of) about the general claim that we put our infants in the Covenant of Grace (this requires a lot of clarification I don't have time for here). But when we use the words substance and administration, and as they've been used traditionally, that's not what's we're referring to. He's talking about the inward reality versus the outward realm of the covenant. But substance/administration is what is used to distinguish between the Covenant of Grace in the OT and the Covenant of Grace in the NT. They are both the Covenant of Grace; they're both the gospel; IE, same in substance. But they are administrated in different ways. How so? This is where we get into the differences between the OT/NT. The OT was less clear, the NT is more clear. The OT had ceremonies as appendages that were done away with in the NT. The OT was Christ in shadows, the NT Christ in substance. In the OT the gospel had overall a lesser effect on its hearers, a much greater effect in the NT.
To get to his final objections (Inconsistencies, #4):
#1-2. Some have indeed argued that an unbelieving spouse who is willing could/should receive baptism as being part of the household. If any of us had bondslaves the way Abraham did in Genesis (not hired workers for the day but belonged to the household for life); we would also be baptizing them.
#3. I don't really follow him here to be honest. Yes, we only baptize the children of professing believers. An (adult?) non-communicant member means that person grew up in the church but hasn't professed Christ. Which means they haven't personally made a claim to faith (they wouldn't consider themselves a believer; at least not yet). So. . .no, we don't baptize their children. Don't get the objection.
#4. Faith wasn't required for circumcising (Gentile) adults in the Old Covenant? I would say it WAS required. First and best example of an adult believing before receiving the sign is Abraham himself (Romans 4:10-11). He is the pattern par excellence for converting Gentile adults; he believes in the Lord first then receives the sign to signify his faith. There's more: In Ezekiel 44:7-9, the Lord, speaking in particular of Gentiles, rebukes Israelite leaders for allowing foreigners both uncircumcised in flesh AND uncircumcised in heart into the sanctuary. So, the Gentiles who were to be given access to the Lord's sanctuary were not only to be circumcised in flesh—but also in heart. Faith was absolutely the prerequisite for an adult Gentile in the OT who wanted to follow the God of Israel and join His people. Besides, Exodus 12:49 says it was the same rule for Gentiles who joined God's people as it was for Jews. So, if the Lord was so disturbed over the fact that many in Israel were outwardly circumcised but lacked the true circumcision of the heart (Deut. 10:16; 30:6; Jer. 4:4, 9:25-26, etc), how could that be okay for Gentiles?