You need to be checking that is able to cope with all possible installation problems!, that is working under the expected mode of failure with a variation of loading effects and soil parameters(undertake sensitivity).
Always design the pile for 2-3diameters below the fixity point(zero displacemts), even if you capacity checking does not need it.
Understand the effective moduli profiles (especially if you might undergo undrained loading - dynamic soil proporties considerations. Consider the distribution of the load transfer and shear especially. Check if the piles are susceptable to lateral spreading conditions, or you have a clay layer overlying a liquifiable sand or sloping conditions. Undertake a reliable buckling checking, don't go over L/D>50. Introduce any kinematic or interaction effects. Use beam-column analyses for the pile and p-y curves for soil. If soil is silt, silty sand and clayey sand use cohesive p-y curves. If you drive the piles be very careful with your assumptions, be conservative.