I have deconstructed the physics of superheroes before. My approach is to ignore the mutation aspect - to accept the background story that gave the hero his or her powers. My concern is instead, given such powers, is the rest reasonable? For Spider-Man, I'd like to focus on the web that he shoots from his wrist to the buildings of New York City as a principal means of transportation. Can a thin web realistically sustain the tension that manifests within it when Spider-Man swings through the city?
Consider the awesome illustration below (mad 'Paint' skills) that shows the famous web-slinger swinging from the top of a building using web length 'R'.
This result is somewhat surprising. It shows that the maximum tension in the web during a swing from rest is 3mg regardless of the length of the web. Though a longer web results in a greater speed at the bottom, the centripetal acceleration at that moment, 2g, is independent of R.
The pressure, or stress, within the web is the tension force divided by the cross-sectional area of the web:
Let us assume that Spider-Man's mass is 80 kg and that the cross-sectional area of his web is 1 square centimeter. We then find that the stress within the web when Spider-Man is at the bottom of his swing is 23.5 MPa. A spider's web has a strength similar to that of high strength steel, which is about 1000 MPa. So, Spider-man's web should have no trouble sustaining a stress of 23.5 MPa. Even if we double the mass (say he were swinging along with Mary Jane Watson), Spidey's web easily passes the strength test.
Where the web begins to run into trouble is when we consider its weight. The density of web (about one sixth that of steel) is roughly 1.3 g/cm^3. Spidey sometimes spins webs as long as the height of the buildings he swings alongside (say 100 m). The volume of such a web (again we assume a cross-sectional area of 1 cm^2) would be 10,000 cm^3. The corresponding mass is 13,000 g or 13 kg. That is one heavy web, and a disturbing amount of mass to lose every time he takes a swing. I mean, 13 kg is a pretty big proportion of his total mass. I would have to conclude that Spider-Man defies the principle of conservation of mass.
While we're at it, why does his web stay straight as he shoots it? It really should bend according to gravity. Furthermore, it should bunch up.
You may be wondering how I could be so critical of the mechanics of Spider-Man's web, yet overlook the radioactive spider that permanently altered his DNA. I agree, it does not make much sense. But it is a fun exercise, and that is justification enough. If my daughter gets to have fun with Spider-Man, why can't I?