That's what confused me, he survived the winter which would have been hard but struggled to catch food when the snow melted.
I wonder whether he had mental health issues because it would seem he could have done more to help himself.

The film shows him not having many survival skills such as failing to use the moose meat properly and not knowing which plants to eat. Is this accurate?
Only partly. The movie, as a whole, heavily fictionalizes McCandless' story (it says right off the bat that it is "based on" a true story - but it is
not
, itself, a true story). For example, the "seduction" scene with Tracy was
totally
fictitious, and seriously offended the real Tracy Tatro.
As for survival skills, Chris had quite a lot of wilderness camping experience, mostly in the Appalachians as a young teen, and the southwest as a young adult. But he lacked knowledge and experience in the specifics of survival in the subarctic, which was and is challenging in unique ways. The "poison plants" business is also fictitious - Krakauer can't accept that Chris starved to death, he has come up with one wacko theory after another to try to make Chris's death a spectacular and one-in-a-hundred-million event. But he lacks supporting evidence, and has no scientific training whatever. There were no poisonous plants/berries in the vicinity, and since Chris kept a detailed food diary, there's no evidence he ate a surfeit of anything in particular. He did have a guide to edible plants in the area, but the problem there is that those plants did not provide much in the way of needed calories, carbohydrates, and fats.
It's puzzling that, although we know Chris had with him a fishing rod and tackle which the old man gave him, there's no evidence he ever used it to try catching fish, which were plentiful in the rivers at that time of year. That's possibly a survival skill he lacked, as was his inability to properly prepare and preserve the moose meat.
So in hindsight it's easy to see that Chris wasn't properly prepared for his odyssey, though he was better prepared than the film suggests, but OTOH bad luck and an injury of some kind also played a large role in the negative outcome.

The film shows him not having many survival skills such as failing to use the moose meat properly and not knowing which plants to eat. Is this accurate?

That's pretty much true, although there are some outstanding exceptions, such as Dick Proennecke (see
http://www.dickproenneke.com/
.
The film doesn't make this clear, but McCandless had no intention of
staying
alone in the wild. He intended it as a brief sojourn, like a monastic retreat, expected to last around 3 months. He had told Wayne he would be back in Carthage by August, and his notes indicate he tried to leave in July but was thwarted by the high water on the Teklanika and possibly by an injury he sustained (never explained, but mentioned in his note on the bus - also left out of the film).
It is much less weird or unusual to strike off on solitary tripping for shorter lengths of time, though there still remains a certain safety margin in having others nearby or within reach. Chris had made many such solo trips in the past (though not in Alaska) and thus probably underestimated the danger that isolation posed were he to be unable to get out, as seems to have been the case. If he had not been injured and/or physically very weak, he could have walked out as there was a bridge over the river about a day's hike from the bus, and again, unlike the story in the film, he did have a map of the area which showed this and he had probably seen it himself when he spent his first month exploring the area thoroughly.
He could have packed some other type of emergency equipment - flares, for example, or a short wave radio. A cell phone, even though such were available at the time, would not have been of any use in so remote an area.