1) "American management companies can't get money to Australia." Obviously money can be transferred to Australia. Anybody who doesn't do that is a charlatan. Charlatans can exist anywhere. There's no reason to suggest that a PM in the USA is inherently more likely to embezzle your money than a PM on the other side of Australia.
2) Light bulbs. US tenants have the same obligations to replace light bulbs that Australian ones do. As in Australia, if your tenant calls out an electrician to change a light bulb, you can charge the cost back to the tenant.
3) Vacancy rates and having to have everything "new". The same would apply in Australia if you invested in an area with high vacancy rates. There are areas of high and low vacancy rates in Australia and the USA (though admittedly the overall average is higher in the USA).
4) Charging for non-existent repairs, or repairs not required: As per point 1, this is about the honesty of the PMs. You need an honest PM, whether the PM is across the other side of the city, across the country, or across the world.
5) Air-conditioning units are abused by tenants in both Australia and the USA.
6) It's far from universal to have an ice-maker. If concerned about it, simply don't provide them.
7) "Americans don't pay rent." Well, of course they do. They do seem to have a higher rate of rent default, but the landlord has many more powerful remedies available to them in the USA than we do in Australia. So overall, it's no more of a problem in the USA than in Australia.
8) Replacing bathroom floors every few years. I can't comment authoritatively, but it just doesn't sound right. The few landlords and homeowners I've spoken to haven't replaced bathroom floors and all had tiles.
9) Blocked toilets. As per the light bulb issue, if it's the tenant's misuse that has blocked the drains, they have to pay for the unblocking.
10) Cars in the swimming pool. Also not the landlord's responsibility; cost to tenant.
11) Being told you have tenants when you don't. As per points 1 and 4, this is about fraud by your PM, and can happen anywhere.
12) Charges for mowing lawn by city. If a house, the tenant should maintain the lawns, and the PM should ensure they do. If an apartment, you should be paying for regular yard maintenance anyway.
13) Charges for towing. How on Earth could a landlord end up with a bill for towing a car (not owned by the landlord), that's parked on public property? How would the city even know to associate the car with your property? This just doesn't pass the common sense test.
14) City selling your property out from under you. Yes, there are tax lien sales, but there would be registered letters etc sent first, just as in Australia. Of course, you do need trustworthy people looking after your asset and collecting your mail. Nobody I've spoken to has ever heard of the scenario that Rick outlines having happened.
15) City condemning property due to burst water pipes. You do need to be aware of the requirement to winterise and ensure the PM attends to this, if the property is vacant.
16) Can't get a mortgage for properties under $50K. It may be harder, but this is simply untrue. I recall seeing ads for mortgages from $30K, and I wasn't even looking for low-value mortgages.