Shakespeare made no "spelling error".

There WAS NO standardized spelling in Shakespeare's day.

Here's the entire OED entry:

petard, n.


(pI"tA;d, pI"tA;(r)) Also 7 petar, -arr(e, -arh, -arde, -arra, patar, pettar, pittar, -ard. [a. F. pétard, †-art, pl. -ars (1580 in Littré) (= It. petardo (Florio 1598); obs. Sp. petar ‘a kinde of Artillery to batter, lately invented’ (Minsheu 1599), mod.Sp. petardo), f. péter to break wind, f. pet: see pet n.3 and -ard.]

1. A small engine of war used to blow in a door or gate, or to make a breach in a wall, etc.; originally of metal and bell-shaped, later a cubical wooden box, charged with powder, and fired by a fuse. (Now Hist.)

1598 Florio, Petardo, a squib or petard of gun powder vsed to burst vp gates or doores with. 1604 Shakes. Ham. iii. iv. 207 (2nd Quarto) For tis the sport to haue the enginer Hoist with his owne petar. 1609 B. Jonson Sil. Wom. iv. v, He has made a petarde of an old brasse pot, to force your dore. 1611 Cotgr., Petart, a Petard, or Petarre; an Engine (made like a Bell, or Morter) wherewith strong gates are burst open. 1614 Camden Rem. (ed. 2) 241 Petronils, Pistoll, Dagge, &c. and Petarras of the same brood lately inuented. 1627 Drayton Agincourt xxxviii, The Engineer providing the Petar [rimes are, far] To breake the strong Percullice. 1637–50 Row Hist. Kirk (Wodrow Soc.) 511 The noblemen, with a pittard brake up the utter gate of the Castle of Edinburgh. 1670 Cotton Espernon Table, Montereau Faut-Yonne taken by Petarr. 1721 De Foe Mem. Cavalier (1840) 113 By the help of a petard, we broke open the gate. 1849 Macaulay Hist. Eng. iii. I. 322 A third had defended his old house till Fairfax had blown in the door with a petard.

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Both PETAR and PETARD are quite acceptable.

PETARD derives from the French and PETAR derives from the Spanish. Vide supra.

However Shakespeare used PETAR.

And, of course, he was aware of the humorous undertones -- with the alternate meaning -- *ART.

Pogue Gordon ignorantly leaped in and insisted PETAR was WRONG.

Thereby committing...

EGREGIOUS PRATFALL.

KAWHOMP!!!

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And it's WITH his/her own PETAR...

NOT BY or ON his/her own PETAR.

Ergo...

To Repeat...

Diane Poremsky was...

Hoist with her own petar.

Deeeeeelightful!

How Sweet It Is!
--
D. Spencer Hines
Lux et Veritas et Libertas
Vires et Honor
Veni, Vidi, Calcitravi Asinum