Can rewards incentivise shortcuts to be taken which wouldn't be done otherwise? With a rewards-based system, some may be so incentivised by these rewards that they end up losing the end goal of what is meant to be the aim of gamifying otherwise boring, repetitive activities.  

Why do rewards manage to detract users from the example of good behaviours in a non-game environment, and how should implementers of gamified systems work around this issue?
TL;DR
When a boring, repetitive task is being gamed for rewards, there are two things that you need to look at. First, the problem definition and whether it is accurately defined (keeping in mind that autonomy is not lost). Second, the conditions of the reward and what is the actual behavior that is being rewarded.

There are two main factors influencing how effective or ineffective the system is for encouraging a certain behavior and they are:

The Problem Definition
The Reward Conditions

I will use two examples to discuss this problem:

First, the task of folding and putting in envelopes 40 letters.
Second, the task of proofreading 20 articles.

The Problem Definition
The first and foremost thing to look at is the problem itself. We are well-aware of human tendencies well before we even start to define a gamified system and so, I feel, it is the responsibility of the designer to be smart in defining the problem.
In the first example, the task itself consists of folding letters, and then putting them into envelopes. In this, a person may fold a letter in any way, any number of times, and may even just stuff it into the envelope. One way of reducing individuals from succumbing into bad habits is to redefine the problem to: fold letter, put in envelope and seal the envelope. Just this small change will now make it less likely for people to stuff an unfolded letter into the envelope as they themselves have to close it as well.
However, it is important to remember that one of the biggest motivators for gamified systems is autonomy, and over-defining a task will reduce it, thereby reducing the motivation to participate at all.
In the second case, there are multiple avenues by which the actual task can be avoided (read a few pages, read a few papers, etc.). So, its pretty clear, that this task has significant chances of being gamed.
Now, we come to the second factor that affects good behavior in a gamified system and how it can be leveraged to regulate it.
The Reward Conditions
The rewards being offered can be divided into three major types:

Participation-Contingent: The reward is awarded if the individual simply starts the task. In the first case, if the person, just does even one envelope, then he is given the reward. Similarly, in the second case, if the individual proofreads even one paper, he is given the award. This as can be seen will be least effective and promoting good behavior over long periods of time.

Completion-Contingent: The award is given to the individual if he completes the task, irrespective of the quality of the results. That is, all envelopes filled with letters folded (however they may be) and all articles proofread, not looking at accuracy or errors missed.

Performance-Contingent: The individual is rewarded if the quality of the work done is above a certain fixed threshold. None of the envelopes have any bulges anywhere and seal easily, and 18/20 articles are error-free. This is the most effective in preventing individuals from falling into bad behaviors within the system.


Therefore, it is important to think clearly about what the reward is and what is actually being rewarded.
Summary
Be aware of the task and what it requires an individual to do, and also, what a reward encourages and what is the minimum that needs to be done to get it.