I know comparative advantage, but does it really apply to competition with tax rates?

For example inside the European Union it doesn't matter in which country a company is based, you have basically freedom of trade for goods and services. In Germany the medium age is 45 years, in Ireland it is 35 years; Population > 65 years is 20,6% vs.11,6%. Even if all other regulation in Germany + Ireland was identical, it seems unrealistic that Germany could sustain as low a tax rate, since the government has bigger expenses due to demographic issues alone. (Retirement benefits, medical)

If every company moved to Ireland because of the lower tax rate, what should be done with the old people in Germany?

You seem to labour under the illusion that if the money isn't taxed in a particular country, it somehow disappears from that country altogether. Yet wages are paid to employees and profits are distributed to shareholders. Lower taxes allow companies either to lower their prices or distribute more wages and profits. That's generally considered to be A Good Thing. If Germans want a slice of those profits, they can buy shares in the Irish-domiciled companies like everyone else.

Employees and shareholders do not get their money from the government. But what about old people, government employees, social services? It just seems to me that the "assets" of the government move to a low tax country, but the "liabilities" stay the same...

If there was a hypothetical "ZeroTaxCountry", to which companies could declare their allegiance and pay no taxes at all. Would you consider that "A Good Thing" as well, since it seems to have all the benefits you alluded too?

That's what happen when you tie yourself to a company whose business is to tax away income from a movable source. Economics is about learning the rules of the game, not changing it. If it could be changed, than the economists would look for what can't be changed. And then optimize for that.

As if it is good thing the company moving to a no tax country. From the point of view of the company's clients, it actually would, since it would mean that its products have the potential to be the cheapest of the market.

You're right that future liabilities are a mess. In Australia in the early 1990s the government introduced a program of compulsory superannuation. Already something like a trillion dollars has been saved by Australians against their retirement under the scheme. Singapore does something similar. Australia has also put away tens of billions of dollars against the future liabilities of public service pensions.

Will it completely do away with government liabilities? No. Australia too will face higher health care costs. But some of those costs will be defrayed by the superannuation and taxes levied on an economy that grew faster without the taxes than with them.

I am ambivalent about the Euro-US situation. On the one hand, it sucks that you face a period of painful adjustment to inescapable economic reality. On the other hand, your politicians have steadfastly refused to face up to those realities. As an Australian I find it annoying that profligate governments in Europe and the USA are hurting my prospects, even though here we've largely enjoyed fairly sensible economic policy for the past 25 years.