Broadcom recommends a 4-layer PCB with a solid ground plane, and thermal vias under the device to dissipate heat. A thermal pad on the bottom of the device should be connected to a thermal plane on the PCB.
To optimize for low power consumption, use the lowest possible supply voltage, reduce the clock frequency, and use the device's power-down modes. Additionally, minimize the number of active circuits and use a low-power oscillator.
The HSMP-3864-TR1G has built-in ESD protection, but handling precautions are still necessary. Use an ESD wrist strap or mat, and handle the device by the package body, not the leads. Avoid touching the leads or any exposed die.
The HSMP-3864-TR1G is rated for commercial temperature range (-40°C to 85°C). For harsh environments, consider using a more ruggedized version of the device or taking additional design precautions, such as conformal coating and hermetic sealing.
Use a logic analyzer or oscilloscope to capture waveforms and debug the issue. Check the device's configuration and programming, and verify that the PCB layout and power supply meet the recommended specifications.