@joydada,
Given the context, I think it would be hard to misunderstand the intended meaning here.
The supposed ambiguity seems to be whether (1) "there is a can with a hole" (i.e., two things next to each other--say a hole in the ground with a can next to it) or (2) the can has a hole in it.
To be absolutely clear, you could simply say "The is a can with a hole in
its bottom (instead of
the bottom). That specifies where the hole is and now "bottom" can only refer to the bottom of the can itself--not some other "bottom" like maybe the "bottom cabinet."
But, there's no real way to make sense of "bottom" here unless it refers to the bottom of the can, so I don't really see a problem with the original sentence.
As a matter of principle, though, you should be clear about which words or phrases are modifying what items.