So, after exploring a bit, I ran across some weapons you cannot infuse. It's quite strange, since almost any weapon can be infused, even those which already hve elemental damage or aux. effects. From the information I have gathered, the only weapons that can't be infused are Mytha's Bent Blade, the Scythe of Want and the Moonlight Sword.

First, Mytha's Bent Blade is said to inflict toxic as well as poison.
Moonlight Sword is said to have been removed from the list of weapons you can infuse since the last patch (probably for balance purpose, since an infused Moonlight Sword was insanely strong)
Then there is the Scythe of Want and I don't really know this weapon well.

From the informations I have on Mytha's Bent Blade, it appear that a weapon that already have a double effect (poison and toxic, in this specific weapon) negate the possibility to infuse. It seems that a weapon can have two "enchantments", one already existent and one from the infusion... If the weapon already have 2 special effects, then the infusion can't be applied. It's purely speculation, as I have no proof, nor extended testing behin me, to say that.

But, considering that theory, that makes me ask one question : the Scythe of Want, what special effect does it have, to negate the infusion possibility ? It already does darkness damages, but what else ?

Are there any more weapons or shields that can't be infused or is that all ?

From the fextralife wiki "the weapon's higher than normal base damage allows one to forgo weapon enchants. In fact, this weapon will likely have a higher AR than similar weapons with Resonant Soul Weapon. This can save attunement slots for another spells." Not sure how useful that is but maybe it helps