BTA has added a bevy of custom shortcuts for your convenience and usefulness. The ones we've done are added below for your edification.
Movement and Map UI Indicators
Holding Left Alt + Move Mouse on Terrain: This lets you see the movement nodes around your cursor. Not amazingly useful but lets you see dropship landing locations and terrain types.
Movement - Hold Left Shift + Click Movement: Lets you select waypoint movement (only on walk by default, requires Lightfoot to do on a sprint).
Unit Indicators - Left Ctrl + A: Cycles through all Aura display modes (default, show all, hide all).
Unit Indicators - Ctrl + T: Enable/Disable attack direction indicators.
Selected Unit - N: Cycles through abilities added by equipment, such as BA swarming.
Combat - With Attack Ground selected, hold Left Alt: Allows you to friendly fire allied units. Note: you do not receive salvage for allied units.
Combat - Hold Ctrl while dismounting a building with Battle Armor: When you click dismount, the BA will now dismount to the roof.
Unit Weapon Panel
Weapon Panel - Left Ctrl + Click Ammo: Ejects ammo.
Weapon Panel - Left Shift + Click Weapon Name: Enable/Disable all weapons with the same name
Weapon Panel - Left Shift + Click Weapon Ammo: Sync ammo for all weapons with the same name
Weapon Panel - Left Shift + Click Weapon Mode: Sync mode for all weapons with the same name
Action Button Modifiers
Ctrl + Brace Button: Will open dialogue to enable/disable individual heat sinks. There is no benefit to doing this in BTA.
Shift + Brace Button + Shift: Will reserve currently selected unit to the final phase of the turn.
Ctrl + Sprint Button: Will open a dialogue to scroll through and play voice lines for that pilot.
Mechlab - Ctrl + Max Armor: This will enable the stupid vanilla-style max armor functionality that doesn't actually work don't use this.
Mechlab - Ctrl + Strip Equip: Will only strip weapons and ammo.
Mechlab - Shift + Strip Equip: Will strip all "grey" equipment (actuators, heat sinks, engines, gyros, upgrades, etc).
Mechlab - Shift + Armor Increment: Will increment armor by 1 point up or down instead of 5.
Salvage Screen - Shift + Click on an item you have received (not a mech/tank part): Will sell the item from that screen.
Starmap - Ctrl + F: Opens a search bar. Can search by planet name or planet tag.
Starmap - Shift + Click on system: Allows you to set waypoints for planetary travel.
Starmap - F1: Shows only un-visited systems.
Starmap - F2: Resizes map dots by System Difficulty rating. Larger is higher skull rating.
Barracks - Ctrl + Click SERVICE RECORD tab: Allows you to reset OpFor Specialization, Mission Specialization, and (if the commander) the StratCom bonuses.
Barracks - Shift + Click SKILLS tab: Allows you to retrain pilots (costs c-bills, requires Training Module 2).
Argo Screen Timeline - Shift + Click timeline item: Advances timeline and stops at that specific event. Will stop if other things pause the timeline before that item (events, bills, etc).