During the 2008 crash/crisis, did ETFs track close to their underlying "holdings"?

An ETF is subject to intraday mispricing as its price can deviate from the underlying NAV. When this occurs, an arbitrage is possible. The most common resolution is via the creation and redemption mechanism where an authorized participant (AP) buys securities in equivalent proportions of the underlying index and receives ETF shares in return. The reverse is done during the redemption process.

Another ETF arbitrage strategy is pairs trading which involves taking a long position in one ETF while simultaneously taking a short position in a similar ETF based on the same index.

And while I'm not familiar with it, I surmise that there would also be a possible arb between the ETF and the respective futures.

In general, the ETF's price is going to track the market fairly closely with the NAV except in very volatile markets (for example, 2008). While the same arbs apply, the spread may be larger, briefly.

Inverse and leveraged ETFs track fairly well in the short term directional market. But in oscillating markets and over longer periods, there's beta slippage as well as the cost of the leverage. You can see this by comparing historical prices. IMO, if you get the direction right, it's not the end of the world to get a 2.5x or 2.75x return from a 3x (or -3x) leveraged ETF. However, 3x hurts if you're wrong way Charlie.