What Projectiles can Mario/Dr. Mario's Cape Reflect?

According to this forum, the cape can deflect all projectiles:

Mario's cape can reflect literally any projectile (like Villager's bowling ball and falling tree, and Megaman's charge shot) that isn't an explosive. Explosives tend to explode when hit by the cape, but the damage is reflected.

Although the forum appears to be talking about a different Super Smash Bros, I believe it upholds, since the cape is considered a reflector (see below). The thing with explosive projectiles is that they will blow up instead, but the damage is reflected. In my time playing Melee, this is how I remember it as well.

According to the Wiki page for reflection, the cape is considered a reflector. On the same page, it lists all items that are able to be reflected, including character abilities and the environmental projectiles. Ignoring those, it states in the table for items that "All Thrown Items" are reflectable.

According to the link you added in your question, the only ability I see that may not be reflectable is Sheik's Vanish ability, which is considered a projectile according to that page. There are a few others in that list that aren't, but they are for characters that do not exist in Melee.