I've been playing Diablo (without Hellfire) multiplayer and 4 items glitched out when I tried to pick them up. Nothing of value so far, only a potion, a heap of gold and some non magic armors. It always went down like this: I clicked on the item on the floor and first nothing happened and when I clicked for a second time, the item just vanishes without it being added to my inventory. I played singleplayer yesterday and nothing like this happened.

Has anyone experienced something similar?

Yup, it's a common flaw of original diablo. Were you playing alone? If no, sounds like desync.

Huh, strange. I never noticed this when playing Diablo from my CD all these years. And yes, I have been playing the multiplayer mode alone when I "lost" those items.

Feel free to try https://github.com/diasurgical/devilutionX
We've fixed a lot of bugs so it should work better than the original in every aspect