How objective are scientific measures of paraphilia? Paraphilia (from Greek para = beside and -philia = friendship, meaning love) describes the experience of intense sexual
  arousal to highly atypical objects, situations, or individuals.


Which practices that have been defined as paraphilia has changed over the course of time and with changes in "religious" control over modern society and so a freedom of moral conscience. A striking example being homosexuality, which was considered a mental illness. The educated and enlightened thinkers of many communities now find such an idea as abhorrent. 

What is acceptable sexual practice varies across cultures. This in part is reflected by the age of consent across nationalities; which range from 12 to 21.
Striking disparages showing in the Phillipines where female to male age of consent is 12 and 18 for female to male respectively; but for any   male to male or female to female sex is 18. And in Burkina Faso  where the age for female to male sex is 13 for both sexes, but for male to male or female to female is 21 for both. Not to mention the places where homosexuality is illegal.

Given this great variation is what is legally acceptable (thereby one would conclude socially acceptable within that culture) and what one place would deem as acceptable another would deem as aberrant. 

How can paraphilia be, scientifically, defined on behaviour alone?
Are there neurobiological differences between the brain of a "paraphilic" and a "normal"?
 What is the correlation between other mental illness and/or abnormal psychology and paraphilia?

note: this lends itself to what we define as illness or abnormal psychology
wiki's Psychopathology page should give you some insight into this issue.
First, you must realize that a psychological illness is generally different than a biological illness. The difficulty when dealing with most (not all) conditions included in the APA's DSM (Diagnostic and Statistical Manual of mental disorders) is that there is no truly objective way of determining whether something should be considered a disorder. This is why they use the 4 D's to determine whether the thing someone is experiencing is a disorder.
It is not truly a paraphilia unless the behavior includes a combination of the following: highly statistically deviant, causes distress, causes the person to not be capable of doing things they normally would be able to, or causes danger to others.

Deviance: this term describes the idea that specific thoughts, behaviours and emotions are considered deviant when they are unacceptable or not common in society. Clinicians must, however, remember that minority groups are not always deemed deviant just because they may not have anything in common with other groups. Therefore, we define an individual's actions as deviant or abnormal when his or her behaviour is deemed unacceptable by the culture he or she belongs to.

(There are moves to start avoiding using this as a reason because of the complexity and it's apparent arbitrariness, but that's a different issue)

Distress: this term accounts for negative feelings by the individual with the disorder. He or she may feel deeply troubled and affected by their illness.
Dysfunction: this term involves maladaptive behaviour that impairs the individual's ability to perform normal daily functions, such as getting ready for work in the morning, or driving a car. Such maladaptive behaviours prevent the individual from living a normal, healthy lifestyle. However, dysfunctional behaviour is not always caused by a disorder; it may be voluntary, such as engaging in a hunger strike.
Danger: this term involves dangerous or violent behaviour directed at the individual, or others in the environment. An example of dangerous behaviour that may suggest a psychological disorder is engaging in suicidal activity.

So no, a paraphilia cannot be scientifically determined by behavior alone (just like the idea of love cannot be proven scientifically by behavior alone).
In short, paraphilia (just like most psychological illnesses) is definitely somewhat subjective. From a clinical standpoint, they're just a way of categorizing and defining disorders that people deal with, like happiness or sadness, not a scientific definition like whether or not someone has cancer.