When Janeway and others approach the statue seen from behind, she suddenly has blonde hair instead of her brown hair.
Tom tells B'Elanna that there were no TV remote controls in the 1950s. In fact, the very remote she gives him - the Zenith Space Commander - was invented in 1956, and there was at least one other in use at a year before that. Wired remotes were also around at least by 1950.
When Tom tells B'Ellana that televisions didn't have remote control units in the 1950s (which is incorrect itself), she tells him that she took some "poetic licence" and hands him a remote. She obviously meant "artistic licence".