After Dexter wakes up after spending the night on Rita's lawn chair, the sweat stain on his shirt keeps appearing and disappearing.
Dexter is wearing disposable gloves while preparing blood samples from the trophy slides for testing. He is in the lab that is inside the police station. He exits the lab by touching the door handle, walks into the bullpen, then strips his disposable gloves and throws the gloves into a common waste basket that is next to a desk.
Dexter should have disposed of his gloves in a biohazard waste bin that was inside the lab, and before touching the door. (Never mind the rest of the PPE he should have been wearing at the time or that he should have donned new disposable gloves between each sample to avoid cross-contamination).
It makes little sense for Doakes to take Dexter's slides out of the apartment. By doing so, he made them worthless in terms of evidence because it was an illegal search and there was no official chain of custody. All it did was alert Dexter, which could even have made him flee and go under ground.
Doakes throws away the SIM card from his phone but it's not enough if he wants to really hide - the cellphone itself can be traced even without a SIM-card.
It is not plausible that Dexter should be able to overpower Doakes, no matter how much karate he knows. Doakes is stronger, better trained and has a gun on him while Dexter is in handcuffs and gets shot in the leg early in the fight.