While this has already been well described, I feel the need to emphasize just how very alien the experience of being a spider can be, and how dramatically that can affect a druid assuming that shape.
The first example is of course senses.
Most spiders have rudimentary sight at best, seeing on a matter of single digit inches or even millimeters, and at that distance only fuzzy indistinct images.
If we limit ourselves to jumping spiders and webcasters, the best visually that I'm aware of, we still find sight radically worse than what one would imagine, moving up to the "foot or two" range as far as I'm aware.
This means that, for looking around, a spider is more comparable to a humanoid in a moderate fog, if you scaled them to match, for visual range. In practice only the biggest most visually acute spiders would even be able to see neighboring squares of movement.
It also makes every square a spider travels mysterious, exciting, and scary. Which can be pretty cool.
The spider experience of sound has little to nothing to do with our own. In practice even sounds we would consider very high pitched are well into "infrasound" and is well outside of the lived experience of most spiders.
Instead they focus on the currents of air sensed by their body hair, (an experience vastly beyond the primitive imitation we humans experience when feeling a breeze) and the tremors passing through the ground they stand on (think jurrasic park, but a large beetle is the size of a t rex and humanoids are just stupid big).
While spiders have a variety of other useful senses they are all optimized for ranges well below what a humanoid would find valuable. The larger spiders, megalomorphs, are relatively short sighted and easy to spot, while the most visual spiders, jumpers, are tiny and their idea of "long range" is a foot or two.
Wolf spiders, the fastest spider of humanoid scales as far as I can tell, reach "up to" 0.02 miles per hour under any sort of sustain. Compared to a human cap of something like 6 miles per hour (a "great" marathon pace). At those speeds travelling across a room should feel like... 300 times as big. ^_^
Each room for a human is a huge dungeon for a spider. Travelling through it could be cool and all, but still.
The Hard Answer
I, and my table, are very motivated by the "unexpected bit of realism" and would enjoy a druid suddenly finding out just how freak'n hard a spider's life really is. Hours of play describing arduous travel, tense escapes, and vague descriptions that the players try to, somehow, transcribe into a map could lead to a ton of fun.
But that creates a "main character sub story" which is a major issue in and of itself.
The easy answer
Tell your player you aren't digging how this is working out, and ask what compromise they would consider reasonable.
Often a player using a technique like this feels that something is being interpreted wrong, or is "broken", themselves. Asking them "What am I (as the DM) getting wrong here?" will often pull a player across the table and their answer will fit them, and the table, better than anything those of us on the net have.