Would minimizing influence into the world be a safe directive to a general AI? Let's take our standard paperclip maximizer General AI and attempt to obtain precisely one million paper clips, over course of a year, without destroying the universe in the process.

Most maximization directives make the process run-away. As cheaply as possible will crash world economy. As good clips as possible will turn the universe into super-synthesizer that assembles atom-perfect paperclips. Adding a deadline on these maximization processes will probably result in terrorizing the staff into readjusting the deadline, or invention of time travel (after consuming the solar system to invent it.) Minimizing resource usage would likely result in closure of all industry world-wide. You know, the standard horror scenarios.

What about the directive of minimizing AI's influence on the world while completing the task? Would it be safe, or can you spot a runaway scenario where it could result in dire effects?
I like mindrime's answer as it identifies fundamental, applicable notions.  I'll attempt another short answer from a Game Theory perspective.

Game Theory was founded in the minimax principle.  Specifically, maximizing benefit while minimizing potential downside in a condition of uncertainty.  

Minimax works very well in contexts with easily definable parameters, such as combinatorial games and procedural optimization, but it gets more tricky in real-world scenarios where too many parameters may be present, resulting in a combinatorial explosion. 

Another issue regarding real-world applications arises from the symbol grounding problem.  In the paper clip scenario, the benefit sought (the goal) is clearly definable, and can be expressed mathematically.  By contrast, the downsides to be avoided are more difficult to define: "Don't destroy the world", "Don't use up resources to a degree that humans suffer", "Don't harm the environment" all rely on language.  This is to say they rely on terms that, at present, constitute symbols that cannot be grounded.  Thus there is room for misinterpretation that may yield unintended consequences.

"Minimizing impact on the system" (minimizing influence in the world) would be the goal, but how do you guarantee an automata has a clear understanding of what this entails in every possible scenario?