The second movie did a better job of showing Peter's smarts, but the first only had people talking about it -- a mortal sin in moviemaking. In fact, the most "smart" scene was when Parker tells Osborn he has read on of his papers -- which several civilian friends of mine, bringing no backstory into the theater with them, took as Peter BSing to impress Norman. And the first movie is, of course, the one in which it is most important to show Peter's smarts, in terms of establishing the character -- unless you're Sam Raimi.

Apparently you have no idea how long it takes to patent and copyright an invention -- even assuming you have a lawyer who will do the work for free, up front.

I can attest to that.  Even if Peter had a lawyer working for free, the USPTO has many filing fees as well as renewal fees (once it's patented) and it can take years before a patent can be issued (and that's if someone else hasn't already invented something analogous).

I always liked the mechanical webshooters.  When he'd run out of web fluid in some issues, Spider-Man had to be more resourceful in overcoming the obstacle.  Plus, as a kid, I thought it was a "cool" device.

Peter Parker: So is that it? (referring to Octavius' invention)   
                   
Otto Octavius: Yes. My design to initiate and sustain fusion.
                      
PP: I understand you use harmonics of atomic frequencies.

OO: Sympathetic frequencies.

PP: Harmonic reinforcement?
                
OO: Go on.
                 
PP: An exponential increase in energy output.
                  
OO: A huge amount of energy. Like a perpetual sun providing renewable power for the whole world.

PP: Are you sure you could stabilize the fusion reaction?
           
OO: Peter, what have we been talking about for the last hour and a half? This is my life's work. 
I certainly know the consequences of the slightest miscalculation.
             
PP: I'm sorry. I didn't mean to question you.