For example, compare South Pole Telescope (Q1513315) with South Pole Telescope (enwiki).
On Wikidata, the construction time (qualifiers of statement “significant event: construction”) is November 2006–February 2007; in the Wikipedia template, which gets its data from Wikidata, it is instead October 2006–January 2007.
In general, the date on Wikipedia appears to always be one month before the date on Wikidata; it even rolls over the turn of the year correctly (January 2007 → December 2006).
You can also reproduce this on the Sandbox (Q4115189 / Wikipedia:Wikidata/Wikidata Sandbox) by adding a statement “significant event (P​793): construction (Q385378)” with start time (P​580) and/or end time (P​582) qualifiers to the sandbox item, and adding {{Infobox telescope}} to the sandbox article.
This only happens for times with precision “month”; both date and year work fine.

I think this issue is part of T87764, but I’m probably not allowed to set that.

See also T107870: Illegal dates in date type

PS: What’s the usual way to prevent autolinking of Wikidata property numbers P​123 to Phabricator pastes? I put a zero-width space between the P and the number, but that’s not very convenient :)