I have always been able to enter build mode from the map view even when a lot is marked as incomplete (with the triangle and exclamation point symbol you describe). You just can't travel there with a sim. You should be able to enter build mode from the map and check if anything is missing from the required list.
I have had issues with kleptomaniac sims stealing objects that are needed for the lot to function (this can happen even if you don't have Eco Living's NAPs). I ended up using one of LittleMsSam's mods to ban kleptomaniacs from most community lots.