For a contract to be formed, it is said there must be a "meeting of the minds." Does this mean that the fact-finder attempts to ascertain the actual subjective intentions and understanding of the parties?
No: "meeting of the minds" (also known as consensus ad idem) is not about what the parties actually subjectively understood or wanted.
For contract formation, consensus ad idem only requires that it appears to an objective reasonable person that the two parties were assenting to the terms of the agreement. See generally, Westlaw Canada, "Contract: I.2: Consensus Ad Idem"; see also Cornell Law School, Legal Information Institute, "Meeting of the Minds."
"[I]n contractual interpretation, the goal of the exercise is to ascertain the objective intent of the parties (Sattva Capital Corp. v. Creston Moly Corp., 2014 SCC 53 at para. 49).
"Evidence of one party’s subjective intention has no independent place in this determination" (Eli Lilly & Co. v. Novopharm Ltd.,  2 S.C.R. 129 at para. 54).
It is important to note that consensus ad idem is an objective, not a subjective test. As noted by the Alberta Court of Appeal in Ron Ghitter Property Consultants Ltd. v. Beaver Lumber Company Limited, 2003 ABCA 221, at para. 9, the test is whether “it is clear to the objective reasonable bystander, in light of all the material facts, that the parties intended to contract and the essential terms of that contract can be determined with a reasonable degree of certainty.”
(Silver Eagle Management Inc. v. Onoway (Town), 2011 ABQB 139 at para. 60).
Though the courts now have clearly adopted an objective approach to the analysis of contract, they occasionally use language that suggests that what is subjectively in the minds of the parties is important. It is sometimes said that there has to be a consensus ad idem (in Latin, literally “agreement to the same thing”) or that the parties “minds have to be at one”. Statements like this are misleading. No legal system can require that there be an actual “meeting of the minds”, for that would provide too much of an incentive to those who would like to contract with their “fingers crossed”. The requirement that a subjective agreement exist would permit one party to stay with a contract only so long as it suited its convenience; when it did not, the party could claim that it had never really agreed to the other’s terms.
(MacNeil v. Dana Canada Corporation, 2008 CanLII 35689 (ON SC), at para 13, quoting Swan, Reiter & Bala, Contracts: Cases, Notes & Materials).