Here's a silly one: Did Luthien's ear shape change when she returned from Mandos to Middle-earth as a mortal? For that matter: were she and Beren resurrected in the same bodies or different ones? Was Beren's hand restored? Did they just awaken in Middle-earth or have to sail there from Mandos?
Most probably, they travelled to the Halls of Mandos in spirit only, while their bodies remained in Middle Earth.
The Elves don't actually have pointy ears. The difference between Elves and Men is almost entirely spiritual. The only physical differences are height (Elves are taller) and prettiness (Elves are much better looking than humans).
There are some references to elves having pointed ears in Tolkien's writing, but that's just a minor physical detail; the real difference between the two races is spiritual.
Geographically, I am bothered. If Middle Earth and Aman were connected by The Grinding Ice, why wouldn't the forces of the Valar use that path to make a surprise assault on Morgoth during the War of Wrath? Shouldn't that be an easier route to use?
Why didn't US forces in WWII just march across the polar icecap to Europe instead of using troopships? Same answer.
It's mentioned in the earlier sections of the text that the Helcaraxë is not exactly an easy trip. It's bitterly cold, lacks food(which they would thus have to take with them and baggage trains across fields of snow and ice are far more difficult to handle than supply ships amongst a convoy), it is effectively a constantly shifting glacier making any kind of reliable pre-planned route almost impossible, the terrain is constantly shifting and is implied to a be under regular, if not perpetual assault from snowstorms. The oversea journey, especially angelically enhanced for ease of passage was both faster and easier with much less risk of casualties along the way.
I know its mentioned somewhere that during the journey, many elves died along the way from being crushed beneath suddenly shifting ice. which made me picture it less as a glacier and more a densely pack group of icebergs, all constantly moving about. Its a mark of Fingolfins leadership that he brought as much of his host across as he did.
Besides, when you have Manwe the Vala of Fair Winds and Ulmo the Vala of Following Seas behind you, the sea passage ought to be pretty smooth.
How were the Naugrim able to assassinate Thingol in his own realm and get away with it? Isn't his wife supposed to be a very powerful Maia?
Why didn't Melian, Melkor, the Noldor, etc. trying doing anything about Ungoliant and her offspring? I know that fighting a horde of demonic spiders isn't exactly a cakewalk, but you'd think that one of them would actually try to confront them instead of letting them scurry around Nan Dungortheb. Ungoliant is an enemy of the Valar, poisoned the Two Trees, helped Melkor steal the Silmarils, and tried killing Melkor over those same Silmarils. You'd think that would send half of Beleriand after her. Sure, Melian did set up that Girdle to keep Ungoliant and other enemies out of her realm, but how come the Noldor didn't try going in there with their enchanted blades to chop the spiders up? Since Ungoliant's webs can be destroyed by fire, why didn't Melkor send any fire-drakes and Balrogs to burn the place down?
After producing her offspring in the Ered Gorgoroth, how was Ungoliant able to escape into the South? Those mountains are smack-dab in the middle of Beleriand and surrounded on all sides by lands owned by Elves, Dwarves, Men, and the servants of Morgoth. Surely someone would notice a giant, light-devouring demonic spider (or if she's using her Unlight, an impenetrable black cloud) passing through their territory, especially when those lands are going to be on high-alert due to the war.