Let's say Heath squeaks out a win in 1974. What does his 2nd term look like? What do the unions do to him? Who takes over the Labour Party/
Presuming your talking about the October election as he did just squeak out such a narrow win in the February one. ;)
Well since he was a determined supporter of the EEC and the man who took us in there won't be a referendum in 75 [IIRC on membership] but you could see a head of steam building up for it under the next government.
If he only narrowly wins then he might not be able to do much because that suggests a small majority in Parliament so unless you get some sort of split in Labour or he makes agreements with other parties he would struggle to legislation passed, especially anything controversial. He was a one nation Tory so he's not going to go to the extremes of Thatcherism in selling off resources or mass privatisation or reducing regulation greatly on business. [He was the one who referred to "the unacceptable face of capitalism" in the Lonrho affair and when Rolls Royce in the early 70's became insolvent over the costs of developing the RB211 engine took the company into public ownership for a while until it was back on its feet. ]
There is likely to be further clashes with the unions but how that develops could be difficult to tell. There was a lot of resentment at excesses of union power at the time so possibly this would be reduced after a fight, but without the swing to almost unchallenged power of big business that occurred OTL under Thatcher. This presumes he's able to last a full term and get a good amount of legislation into law.
Labour could see Wilson be replaced as leader as he has now lost two elections in a year. Not sure who would end up in control, especially as the union block vote was still dominant in leadership elections at the time. You might see a more extreme leader elected as a result, say Foot coming to power earlier, which is probably going to be bad for Labour. Or you could see the more moderate unions realise they need a more centralist leader and someone like Healey or Jenkins becoming leader. Or possibly even an earlier split, although this may be unlikely unless say Foot is elected and the right of the party decides they need to break away, leading to an earlier SNP equivalent.
If Health manages a full term with some success it could basically kill off Thatcherism, at least for a generation or so and she's remembered as a hard right leader most notorious for ending free school milk for junior schools. This, especially if the unions are reigned in but big business isn't given far too much power, could be very, very good for Britain. You could see a steady economic revival, under either party if decently run and North Sea oil used to help this rather than wasted on subsiding Thatcherist failures in the 1980's OTL. You could also see him win another election if Labour is either led by someone like Foot or deeply divided.
If Labour gets a decent leader a lot depends on if Health's government can last a full term and what success he has. If the country is still struggling economically Labour could well win. If their still willing to offer a referendum on the EEC that would also be a big boost for them. However if Heath manages to get economic reforms and a decent measure of success the Tories could still win what would effective be a 2nd term - discounting the Feb-Oct one.