The one pre-battle decision the Union high command gets the most grief for seems to be the decision not to entrench prior to the battle. This is not completely fair as entrenching was not yet a huge part of Civil War life. By 1864 there would not even be a second thought, the men would entrench as second nature. In 1862 though no one would have thought to automatically entrench and orders would have had to been issued to do so.
There was a belief among some in the Union high command that entrenching ruined the offensive capabilities of the army. This belief would be completely gone by 1864. There was also a belief among the Union commanders that they would have to go to Corinth for the next battle, that the Confederates did not have the capability to attack them. It is unclear how the decision not to entrench was made. There is evidence that some Union regimental commanders did ask for shovels and axes to construct entrenchments but they were rejected. Whether this rejection was based due to a lack of such implements or because the high command wanted no entrenchments built is unclear.
There were good engineers with Grant's army and it would have been easy to make entrenchments, assuming there were adequate tools on hand. If Grant had decided to entrench it probably would not have taken long to obtain such tools as he had roughly 100-120 boats moving men and supplies on the Tennessee River.
If the Confederates had attacked a well entrenched Union foe it may have been a much shorter battle. Even if the Confederates broke that line they may have lost too many men to allow them to assault a secondary defensive line.
Having entrenchments probably would have assured the Union of a victory on April 6. Not erecting them was a critical decision. But to be fair entrenching in 1862 would have been viewed as an unique decision.