Check to see if an array is already sorted?

You can compare them two by two:

[["a", 3],["b",53],["c",2]].each_cons(2).all?{|p, n| (p <=> n) != 1} # => true

It looks like a generic abstraction, let's open Enumerable:

module Enumerable
  def sorted?
    each_cons(2).all? { |a, b| (a <=> b) <= 0 }
  end
end

[["a", 3], ["b", 53],["c", 2]].sorted? #=> true

Notice that we have to write (a <=> b) <= 0 instead of a <= b because there are classes that support <=> but not the comparator operators (i.e. Array), since they do not include the module Comparable.

You also said you'd like to have the ability "to check for order based on some arbitrary parameter":

module Enumerable  
  def sorted_by?
    each_cons(2).all? { |a, b| ((yield a) <=> (yield b)) <= 0 }    
  end
end

[["a", 3], ["b", 1], ["c", 2]].sorted_by? { |k, v| v } #=> false

Using lazy enumerables (Ruby >= 2.1), we can reuse Enumerable#sorted?:

module Enumerable  
  def sorted_by?(&block)
    lazy.map(&block).sorted?
  end
end