“Moshe blessed them…” (39; 43)

Rashi explains that the blessing was ‘May it be G-d’s will that He rest His Shechina (presence) in your handiwork’ (in other words in this Mishkan that you have made).
Why did they need this bracha? G-d had already promised them “Make for Me a Mikdash, and I will dwell in your midst” (Terumah 25; 8). Based on this promise the people should have been sure that the Shechina would rest in the Mishkan even without Moshe’s bracha.

Perhaps we can explain based on the Yalkut (Midrash) on Melachim (I 6; 7) on the verse “the House (Temple) when it was built…”. This teaches that a large portion of the work was done miraculously by the shamir worm (which would cut through solid materials by crawling over them). Many of the stones and gems were cut to size using this shamir worm, and they would miraculously be cut to exactly the right dimensions. This is the meaning of ‘when it was built’, by itself. This miracle showed G-d’s close connection to the building of the Temple.

In the construction of the Mishkan there were no public miracles like this. All fo the cutting of materials had to be done by the people themselves. Moshe was concerned that perhaps the fact that G-d did not provide miracles for the construction showed that He was not completely happy with what they had done. Therefore Moshe was concerned that perhaps the Shechina would not dwell there, in the construction that they had made themselves.

Alternatively, we could explain based on the wording of the bracha, ‘the Shechina should rest in your handiwork’. Perhaps it is not referring to the totality of the Mishkan, but rather to each individual part of its construction. He blessed them that everything that they did should be done with blessing. This is similar to the phrase we say in the ‘Mi Sheberach’ – ‘G-d should send blessing on all the works of your hands’. The phrase ‘cause His Shechina to dwell’ sometimes applies to success, like we find in the Gemara (Shabbat 56a) on the vese “David behaved himself wisely in all his ways and G-d was with him” (Shmuel I 18; 14) – this means that the Shechina was with him, and everything that he did would turn out for the best. Perhaps this is what Rashi means also, when he uses the language of ‘blessing’ to describe Moshe’s prayer.