No. The observations need to be repeatable and it adds weight if others can observe it as well. For instance, I can observe a force pulling me down at all times. Now, the source of this force is highly debated, but we can all observe it and we cal all observe it over and over. If only I saw a flying orange dolphin once in my life when I knew I was under the influence of a hallucination, then I would be inclined to not believe it was real.
Also, as far as I know, there is no such thing that allows people to read others minds. LSD included. As for seeing into another dimension, I would have to know how you are defining the word dimension. I regularly look into the second dimension and my mind constructs a third dimensional model from that information. Arguably, I can even look into the fourth dimension. If you are talking about the dimension that Species 8472 lives in, and assuming viewing of this dimension is possible, I can not see why you wouldn't be able to do it under the influence of LSD. However, the sole act of ingesting LSD has not yet been demonstrated to grant the user the ability to view another dimension on their own.
I hope this helps.