Well, there's a reconstructionist preaching at a conference that is popular among the flock that I pastor, so I'm having to answer the question "what's wrong with reconstructionism?" more for a season.
There's much more to say than the following, but here's one of the primary answers: reconstructionism and dominionism miss that Jesus is the last and obedient Adam. Gen 1:28 has already come to fulfillment in Matt 28:18.
Our duty is not to complete the taming of nature (which is impossible until the resurrection, Rom 8:19–23) or take over nations, but to declare the Lordship and Kingship of Christ and the terms (Matt 28:19) upon which He graciously takes (redeems!) subjects to Himself.
It is the Mediatorial Kingship of Christ that fulfills the dominion mandate over all nations (cf. Ps 72) and all nature (cf. Ps 96, 98). Shall all kings submit to him? Absolutely! And we should declare His gospel and law to them (and, incidentally, to every creature, Mark 16:15). But if we encroach upon His own Mediatorial Kingship under the name of dominionism, we make the civil counterpart to the ceremonial error of encroaching upon His own Mediatorial Priesthood as the papists do.
One may reason that reconstructionism comes in different flavors, and that the one they are being exposed to is milder. If so, praise God for that. But why have someone tell you something, that many others have said well and are saying well, when ending up under him puts you at risk of turning aside into serious error.
Incidentally, the same conference features the man that gave this lady her platform, and he has never publicly repudiated her. Her books became progressively (pun intended) worse, she slandered those who criticized her teaching, and now she's preaching in public worship on the Lord's Day.
I've actually refrained from naming the conference or its host, because historically I love both. But if you happen to know what/when I'm talking about, and are going to attend, please do so with some discernment and some determination not to end up where I've expressed concern that you might.
It's a hard thing when your people want to read or sit under problematic teaching. The main thing, for sure, is so to disciple them through the ordinary means of grace that they develop their own discernment either not to attend or to attend and filter. But at what point do you begin to raise the alarm, and how strongly?
