Militarily the Tet Offense was one of the most complete victories of the war.
It shattered the Viet Cong (coupled with the Phoenix Program, which helped eliminate the competent officers that could have rebuilt it) which left South Vietnam a lot safer. Think pre-surge Iraq vs. post-surge Iraq where the US Army completely withdraws and still the level of attacks doesn't go up much (which is what happened in the early '70s)
The North Vietnamese regular army was crushed, and they were unable to mount successful operations for some time.
In the longer term this meant the withdrawal of US troops still left the South Vietnamese (with lots of US money and air support, of course) the ability to keep South Vietnam quiet and beat the North Vietnamese. See 1972-73 before Congress cut off all assistance.
So—militarily, the Tet Offense was the key moment of the post-US ground troop involvement.
Politically, obviously, it was as disastrous a defeat as militarily it was a victory.
It forced LBJ out of the US Presidential race.
It gave "secret plan to end the war" Nixon the Presidency (with, eventually Watergate, which forced the end of all US support to South Vietnam).
Arguably it killed RFK by forcing him into the race (before Tet began on 30 January it did seem like he would stay out).
Finally, and most importantly, it turned American public opinion against the war. Once that happened the chances for "victory"[1] in Viet Nam were basically gone.
As for the POD—No Tet means the US is getting worn down by the Viet Cong, and the North Vietnamese retain major armed forces. Both are huge downsides, and the Viet Cong in particular will effect the near-future a great deal.
On the upside (if you want troops in Viet Nam), politically this means LBJ will beat McCarthy and in all likelihood beat Nixon in the general election.
As I like to state—Viet Nam was winnable (in a narrow sense, as I outline below) but it wasn't worth winning. Especially since a lot of the really bad domino effects were caused by US involvement—notably the Khmer Rouge.
[1] Victory in Viet Nam is an iffy business. Could the US have won? Depends on how we define it. If you mean by turning the North into a wasteland and leaving the South an intact nation-state run by a corrupt dictatorship then yes.
If you mean "has positive effects for the US in the region" than again, with the Khmer Rouge, boat people, and so forth than yes… but only once you accept the trade-off as regards China, a large Korean style ongoing military commitment (even if it "peaceful" it'll still be more active/dangerous than Korea) and a starving North Vietnam.