Early mechanistic studies from the 1960s elucidated several key points:
# No H/D exchange effects seen in this reaction.  Experiments using CD in water generate CDCDO, and runs with CH in DO generate CHCHO.  Thus, keto-enol tautomerization is not a possible mechanistic step.
# Negligible kinetic isotope effect with fully deuterated reactants (=1.07). Hence, it is inferred that hydride transfer is not rate-determining.
# Significant competitive isotope effect with CHD, (= ~1.9), suggests that rate determining step be prior to formation of acetaldehyde.
# High concentrations of chloride and copper(II) chloride favor formation of a new product, chlorohydrin.
Many mechanistic studies on the Wacker process have focused on pathway for formation of the C-O bond, the hydroxypalladation step.  Henry inferred that coordinated hydroxide attacks the ethylene ligand, an internal (syn-) pathway. Later, stereochemical studies by Stille and coworkers support an anti-addition pathway, whereby free hydroxide attacks the ethylene ligand. The conditions for Stille's experiments differ significantly from industrial process conditions. Other studies using normal industrial Wacker conditions (except with high chloride and high copper chloride concentrations) also yielded products that inferred nucleophilic attack was an anti-addition reaction.
Kinetic studies were conducted on isotopically substituted allyl alcohols at standard industrial conditions (with low-chloride concentrations) to probe the reaction mechanisms.  Those results showed that nucleophilic attack is a slow process, while the proposed mechanisms explaining the earlier stereochemical studies assumed nucleophilic attack to be a fast process.
Subsequent stereochemical studies indicated that both pathways occur and are dependent on chloride concentrations. However, these studies too are disputed since allyl-alcohols may be sensitive to isomerization reactions, and different stereoisomers may be formed from those reactions and not from the standard Wacker process.
In summary, experimental evidence seems to support that syn-addition occurs under low-chloride reaction concentrations (< 1 mol/L, industrial process conditions), while anti-addition occurs under high-chloride (> 3mol/L) reaction concentrations, probably due to chloride ions saturating the catalyst and inhibiting the inner-sphere mechanism. However, the exact pathway and the reason for this switching of pathways is still unknown.
Further complicating the Wacker process mechanism is questions about the role of copper chloride.  Most theories assumed copper does not play a role in the olefin oxidation mechanisms.  Yet, experiments by Stangl and Jira found chlorohydrin formation was dependent on copper chloride concentrations.  Work by Hosokawa and coworkers yielded a crystallized product containing copper chloride, indicating it may have a non-innocent role in olefin oxidation. Finally, an ab initio study by Comas-Vives, et al.  involving no copper co-catalyst found anti-addition was the preferred pathway. This pathway was later confirmed by copper-free experiments by Anderson and Sigman. A different kinetic rate law with no proton dependence was found under copper-free conditions, indicating the possibility that even small amounts of copper co-catalysts may have non-innocent roles on this chemistry. While these works complicate the picture of the Wacker process mechanism, one should probably infer that this and related chemistry can be sensitive to reaction conditions, and multiple different reaction pathways may be in play.
Another key step in the Wacker process is the migration of the hydrogen from oxygen to chloride and formation of the C-O double bond. This step is generally thought to proceed through a so-called β-hydride elimination with a cyclic four-membered transition state:
In silico studies argue that the transition state for this reaction step is unfavorable and an alternative reductive elimination reaction mechanism is in play. The proposed reaction steps are likely assisted by water molecule in solution acting as a catalyst.