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Why is the Greek debt swap regarded as a success even though some private-sector investors are being forced to take part against their will and even though CDS¹ are going to be triggered?

This swap has been deemed a success, because the voluntary acceptance rate by private-sector creditors covered 83% out of €260bn in bonds eligible for the swap. If an acceptance rate of at least 75% had not been reached, the swap would not have taken place, and we would have been in a Greek default scenario that would have been far more severe and brutal.
Even so, this voluntary acceptance rate fell short of the target of at least 95% provided under the European assistance plan for Greece. That’s why the Greek government has announced its intention to trigger the collective action clauses (CAC)² that had been recently (and retroactively) introduced into the bonds issued under Greek law. So the small minority of bondholders who had not tendered their bonds to the swap will be forced to do so.
The involuntary nature of the swap resulting from the triggering of the CAC is why the ISDA (International Swaps and Derivatives Association), a professional association governing CDS, ultimately decided that this was a "credit event", thus triggering the CDS on Greek government debt.

Could the triggering of CDS unleash a highly destructive chain reaction, as occurred during the Lehman Brothers bankruptcy?

The risks incurred from the triggering of CDS on Greece look very limited, for three reasons: 1) The market’s net open position on the market for these CDS is only €3.2bn (minus the residual value of the insured bonds); 2) Exposure to these CDS is more than 90% collateralised, according to ISDA; and 3) Unlike the Lehman Brothers case, this event was not a true surprise, and the institutions concerned had the time to prepare for it.

What will this swap’s final impact be on Greece’s private-sector creditors?

The "haircut" on the nominal value of Greek sovereign debt held by the private sector will be about €105bn, based on the nominal discount of 53.5% and a swap acceptance rate of at least 95% (out of an initial €206bn value of outstanding bonds). However, the true loss for private-sector creditors is higher, as the new Greek bonds received in the swap pay out a very low coupon (relative to the discount rate that must be applied to Greece in light of its risk) on maturities of as long as 30 years. Hence, the net present value of the new bonds is far below their nominal value. All in all, the impairment resulting from the swap is estimated at almost 75%, or almost €150bn. Remember, however, that the banks have already set aside provisions on this loss.
This is the largest debt restructuring ever undertaken and is quite unprecedented since the Second World War for a mature economy. So this must remain a "unique and exceptional" event, as European authorities have insisted. It nonetheless now sets a precedent that private-sector investors cannot ignore and that will inevitably alter their assessment of risk associated with sovereign debt in the euro zone and even beyond that.

With this restructuring and the €130bn in additional assistance from other euro zone governments (with, possibly, the IMF, as well), is Greece out of the woods?

The overall objective of the Greek assistance plan is to lower its public debt/GDP ratio to about 120% by 2020 from more than 160% of GDP at the end of 2011.
The debt reduction made possible by this restructuring (incidentally, minus the cost of recapitalising Greek banks to offset the losses on the sovereign debt that they held because, otherwise, they would go bankrupt) is a prerequisite but is far from being enough to bring Greece back to a viable trajectory. In particular, the plan calls for draconian fiscal measures, in order to reach a budget surplus of 4.5% of GDP in 2015 before interest payments, compared with a 2.5% deficit vs. GDP in 2011. But this goal is far from being within reach, especially as there is very little prospect of a return to economic growth.
A first important step is the legislative elections set for late April or early May. Depending on their outcome, we’ll see whether or not there is a sustainable political consensus in favour of the adjustment programme.
In any case, if there was a new restructuring of Greek sovereign debt in the future, it would mainly involve public-sector creditors (i.e., European governments, IMF and the ECB), as they will now hold more than three quarters of Greek debt.

¹CDS (Credit Default Swaps) are derivatives that are like an insurance contract offering protection against a "credit event".

² A collective action clause is a provision that forces all bondholders to accept a conversion of their bonds if a qualified majority of them has voted in favour of such a conversion. In the case of the Greek bonds, the qualified majority had been set at 66% (with a 50% quorum).