The Shamash (attendant) of a synagogue was once caught engaged in inappropriate behavior in the synagogue. The congregation faced the question of whether or not they may continue to use the synagogue for prayer. The terrible offense committed in the synagogue perhaps undermined its unique status of Kedusha (sanctity), which might then disqualify it for use in the capacity of a house of worship.
They brought this question to Rabbi Eliyahu Mizrachi (1450-1526), who ruled (as documented in his work of responsa, #81, {Shaaloth uTeshuvoth, published in two parts- Constantinople, 1546, and Venice, 1647, respectively}) that they may continue to use the synagogue despite the grave sin that had been committed. He draws proof to his ruling from the Chashmona'im's rededication of the Beit Ha'mikdash after the Greeks had defiled it by bringing in idols and statues. The sanctity of the Beit Ha'mikdash far exceeded that of synagogues, and yet the Chashmona'im rededicated the Temple for use after overthrowing the Greeks. This proves that even if the gravest of sins was committed in a synagogue, it may nevertheless continue to serve as a house of worship.
This discussion should serve as an important reminder to us, whose synagogues very often serve as social halls, as well. Given that affairs held in the social hall at times lead to behavior that is unbecoming for a synagogue, we must ensure to close off the area where the affair is held, so that the unique sanctity of the actual sanctuary is preserved. Despite the fact that, as we saw, a synagogue may be used even if a crime was committed there, a community must nevertheless endeavor to ensure that such a situation never arises in the first place.
Summary: Although a congregation must ensure that no inappropriate conduct takes place in a synagogue, it may nevertheless be used for prayer even if it is the scene of a grave transgression.
