Returning is only for thrown weapons, it does nothing for dropped weapons. If your weapon don't have a range increment, it isn't a thrown weapon.
That being said, you have +3 worth of bonuses you could buy. I like ghost touch because doing full damage is better than doing half damage.
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I'm assuming you have Improved Critial (Falchion) as a feat already? Otherwise, Keen is the obvious enchantment to start with.
Is Damage Reduction a thing you have trouble with? Because in that case you may want to consider going for the straight +5, or +3 and Holy.
Other than that, Brilliant Energy sounds pretty badass.
Other than that, Brilliant Energy sounds pretty badass.
Placing Brilliant Energy on an Admantine weapon makes its damage bypass wasted. You use admantine to bypass a construct's DR, but Brilliant Energy is useless vs. constructs.
That said, Dancing at +4 equivalent, is a little too expensive unless you have a crafter in the group. Speed at +3 equivalent is good if you cannot rely on a haste spell being active. Spell Storing at +1 equivalent is good if you can pick a good spell. Mighty Cleaving at +1 equivalent lets you get extra attacks. Heartseeker at +1 equivalent lets you ignore concealment miss chance. Called at +1 equivalent lets you call the weapon back into your hand if in 100', even if in another's possession. Any X Burst at +2 equivalent lets you make the most of your crits.
If you want speed, however, I recommend the boots instead, as they work for all weapons, and won't jack the price of subsequent attacks.
The Pale Green Prism Ioun Stone at 30,000 gp, gives +1 competence bonus on attack rolls, saves, skill checks, and ability checks. Other stones have other things you might want. Dusty Rose Prism at 5,000 gp, gives +1 insight bonus to AC. The cracked version at 500 gp gives +1 competence bonus on initiative checks.
/cevah
I would say Holy, a solid damage boost against the majority of foes and helps overcome a lot of DR.
To be honest, you should be using the Nodachi if you can. It deals 1D10 damage, so it scales better. It has the same 18-20/X2 threat range, the Brace weapon property, and counts as both slashing and piercing damage.
Getting that off my chest, I would refer you to my Two-Handed Fighter guide; specifically, what are some great Secondary Weapon properties.
If you are going to be using the previously purchased Falchion as a back-up/secondary assisting weapon, the best thing you can do is put the Called and Dancing properties on it, and ramp its Enhancement Modifier up to +5 afterward, assuming you somehow can't enhance your primary Falchion anyway. On a surprise round, or before the first round of combat begins, loose the Dancing Weapon, and then proceed to combat. When you get into position to attack, it can make full attacks right away along with you, and if you're good enough, you can shoot enemies running away or pecking at your squishies while the Dancing Weapon cuts up some mooks infront of you. Though it only lasts a few rounds, it falls to the ground, allowing you to bring it back into your hands as a Swift Action, and loosing it again in that same round, making full attacks as soon as you loose it.
Buying elemental or elemental burst properties is a waste of money, considering many creatures by your level will have immunities/resistances to them, making them less worthwhile. In addition, there are more useful properties to buy, and for cheaper. The Courageous and Defiant weapon properties are great starters, and synergize with Improved Iron Will (assuming you've taken that feat, though I suggest you do, since you're a Fighter).
I think when I said Returning I was thinking of Called. We have a Wizard so Haste isn't an issue. I don't have Cleave either so Mighty Cleaving is out the window. I think Speed is probably the best enchant for me, but seeing as how I already have a +1 enhancement I wouldn't be able to afford it. A burst effect of some sort is probably the best bet for me. Maybe Acid Burst.
+1 Speed = +4 equivalent = 32,000 gp = 3,200 pp. You have 3,700 pp, so you can afford it.
/cevah
For the Nodachi, I'd refer you to the Retraining Rules from Ultimate Campaign, as it allows you to retrain all kinds of things into something more desirable. Assuming your GM will allow it, of course... For retraining a single feat, it costs 10 X number of days listed X level. Since you are 11th level, it will cost 550 gold and take 5 days to change out a single one of your feats. Also, don't forget that you can switch out Fighter Bonus feats every 4 levels, meaning the next time you level up, you can take one of the Falchion feats and switch it to a Nodachi feat, assuming you took Weapon Focus/Specialization feats with Fighter Bonus Feats.
You'll need Improved Iron Will for the Defiant's extra usage per day effect to work, since Improved Iron Will gives you the reroll. It's otherwise a very strong +2 property, since it also makes sure you don't drop weapons while stunned and such, and I believe it gives you a bonus on stabilize checks too...
Again, if you are going to make it a secondary weapon, give it the Dancing and Called properties, so you can technically use both that and your main weapon at the same time (or a bow).
A +4 property is difficult to save up for, if not simply obtain in the first place. If you were going to buy properties, I'd save up for the Dancing property first, since applying the Called property next makes it cost that much more to get the Dancing property later.
Falchion to Nodachi is a whopping 0.65 average damage after crits. It's not worth retraining.
Dancing is an effect for people that won't be holding a weapon. It's not for you.
Considering he gets an increased damage dice that's easier to max out and scales better in the long run, count as both Slashing and Piercing for damage reduction purposes, and still retains the other great benefits of the Falchion, it only becomes not worthwhile if he invests in (Greater) Penetrating Strikes, since it reduces all damage reduction points by 10 (and DR/- by 5), and even that's debatable since upgrading to 2D8 or more via Impact property (and/or Enlarge Person) in comparison to at best 3D4 is a great bargain, even more so when he decides to get a Colossal-sized Dancing Falchion cleaving faces.
That's precisely why I didn't say for him to put the Dancing property on his main weapon, because he wouldn't be holding it, defeating the purpose of having a primary weapon. According to his claims, he cannot enhance his primary sword, though it scales with him (I smell 3.X's Weapons of Legacy at work), so he wants to spend money either on other items (it's probably a better solution at this point), or to make his secondary weapon (which used to be his primary weapon) more useful in combat.
Having a Dancing Secondary Weapon making full attacks using your base attack bonus and dealing decent damage while you make full attacks in conjunction makes for the best use of any secondary weapon, period. Is it going to be as strong as you swinging it yourself? No. But it's still increased DPR, and makes for great pre-combat "buffing," so to speak.