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This is one of the eggcorns that show how word choice can slide under the pressure of what could be called the metaphoric potential of a word. For _sphere_ and _spear_, these are quite different: a sphere is a container, homogeneous, round, can grow or shrink; a spear is long and pointed, a weapon.
The substitution _sphere»spear_ can occur as a spell checking artifact, too. But none the less it looks like a genuine eggcorn for at least some writers.
The involvement of rabbits in this idiom seems to be non-obvious to a great many speakers; “hairbrained” gets ca. 10k raw Google web hits to ca. 50k for “harebrained” (1 April 2005). The much more frequent “hair” is giving the rarer “hare” a serious race for its money. The semantics seems to involve hair as inconsequential, fluffy, silly.
See also other “hare”/”hair”-related entries.
James Cochrane, Between You and I, labels this a spelling error. Perhaps it is for some people.
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References to the or an “invincible hand” are common in the contexts of card games and religion. From there they appear to have spread into economics.
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As noted by Ken Lakritz, this is a common error. The search engines turn up hundreds of links to recipes.
It is not entirely clear whether we have a simple hesitation about the correct spelling of _bouillon_. But in this case, we might expect the form _boullion_, which is indeed just about as frequent as _bullion_. To bolster the eggcorn hypothesis we note that bouillon cubes come in an individual gold or silver wrapping at least in some parts of the world, and do slightly resemble miniature ingots.