Normal is also resisted by itself, like everything else. Or put another way, just as many types are resistant to Normal as usual, they're just distributed differently. Notably, Meloetta-Pirouette and the upcoming Mega Lopunny are the only Pokemon that doubly resist Normal, as opposed to in standard play where Aggron laughs off Hyper Voice in spite of its crap Special Defense and Probopass and Bastiodon both exist too.
So yeah, Dragon is garbage now, going from four resistances and three weaknesses (One of which is itself) to one resistance (Itself, which is pretty useless) and two weaknesses. Ouch. Offensively it has two ineffectives and one immunity -so it's Normal, but with a different distribution, but with worse defensive characteristics. It doesn't even get to appreciate being neutral on Steel!
Ghost is, offensively, barely changed, because now it resists itself, which for a lot of Ghosts is basically a good thing, since so many Pokemon use Ghost as coverage. Defensively, it's stronger than ever, resisting itself and Psychic -though to be fair it's lost its Poison and Bug resists, so it's the same number of resists in total, just distributed differently, and with fewer weaknesses.
Fighting has lost its resistance to Bug, but now it resists Steel and Ice, not to mention itself. Nice. Offensively, it hits neutrally on Poison and Bug with no other changes (Barring being ineffective on itself), so that's all upside.
Flying is, defensively, only different for resisting itself. Offensively it pushes past Steel, but is resisted by itself and Ice. Overall a little better defensively and a little worse offensively, given that almost everything is unresisted by Steel anyway.
Poison is now resisted by Psychic but not by Rock or Ghost. That's nifty, offensively. Defensively, it no longer resists Fighting or Bug. Ouch.
Ground is no longer resisted by Bug but is resisted by Ice and Water. Conversely it now resists itself, Fire, and Steel. Ground is fairly happy, at least defensively.
Rock no longer resists Normal, too bad, nor Poison, but now it resists Bug and Ice and itself. Pretty good overall. Offensively, it's resisted by Water, Grass, and itself. Ouch.
Bug no longer resists Fighting or Ground, but now it resists Dark and Psychic, and itself of course. Nifty trade. Offensively, it's no longer resisted by Fighting, Poison, Ghost, Fairy, or Steel, but it is resisted by itself and Rock. Bug is now much better as an offensive type.
Offensively, Steel becomes neutral on Water and Electric, but becomes ineffective against Fighting and Ground. Eh. Defensively, it loses all its resists except to itself, Rock, Ice, Fairy, and its Poison immunity of course. That's 7 resists it's lost.
Fire's offense is no longer resisted by Dragon. Nice. Defensively, it no longer resists Fairy. Fire's pretty friendly to new players.
Water is no longer resisted by Dragon but is resisted by Electric. Fair trade. Defensively, it no longer resists Steel or Ice, but it does resist Ground and Rock. Nifty.
Grass is no longer ineffective against Dragon and Steel. Good for it! Defensively, it now resists Rock but no longer resists Electric. Decent.
Now the only thing that actually resists Electric is itself. Yikes. Of course, Ground is still immune. It's traded away a Steel resist for a Water resist, so defensively it's about the same.
Psychic is now ineffective against Bug and Ghost, but no longer resisted by Steel. Not a good trade. Defensively, it's gained a resistance to Poison, which is nice.
Ice now resists Ground, Flying, Dragon, and Grass, with no loss. (It only resisted itself anyway!) Offensively, it's now resisted by Fighting and Rock, but is no longer resisted by Water, which is a downgrade, but who cares when actual Ice types are so much better!
Dark has no changes defensively. Offensively, it's now resisted by Bug. Minor change.
Lastly, Fairy no longer resists Bug but now resists itself, while offensively Fire no longer resists it but it is resisted by itself.
Basically Ice, Electric, Bug, and Grass are all types to watch out for, while Steel is less defining and Dragon is outright crappy.