The main problem with using random tables is the time they take up, which is exacerbated if one has to roll on them serially, for example because the effect of one table influences another, or because they are printed on different pages of a bound book which someone must flip between the pages of.
The value of a random table in play is the gambling-like suspension of time that goes on between its presentation, the rolling of the dice, its consultation and the announcement of the results. The briefer the time this takes, the more the rollercoaster of emotions it causes are compressed and intensified. The longer it takes to resolve, the more the tension dissolves. As well, the more attenuated any given resolution of this process is from an actual effect, the more the tension dissipates.
"I rolled... 00! Nice. I... must roll on table 3 twice. Oh."
A skilled referee can hold onto some of the tension through table management, but this kind of anticlimax is pretty much the opposite of what you want when you use a random table. And yet the "Roll x times on table y" is an extremely common result to see on random tables.
I would propose that random tables come in two types - those intended to be used outside of roleplaying (though still as part of play), and those intended to be used while roleplaying. The former are character creation tables, world generation tables, treasure tables and other types of procedural generators, while the latter include my potion tables, a lot of the tables Jeff Rients puts up, the traps table in the AD&D 1e DMG, etc.
I generally think the former are less problematic than the later, unless they are used like the latter - rolling up commodity prices manually using the Traveller rules whenever the PCs travel to a new planet in their Type-S Scout Ship is just going to kill everyone's ability to pay attention.
"You see the blue-red orb of Zathis V peeking out from behind crimson clouds below you. Its spaceport looms ahead, surrounded by hundreds of ships of all sizes and types and ages docking and then disembarking for new frontiers. Hold on a sec, I gotta figure out what commodities they have..."
Basically, that kind of procedural generation should be either done before play, or automated on something like an Excel spreadsheet that handles it all for you when you enter in the dice roll. I ran a Traveller game where one of the PCs set that up, and it was a godsend. Otherwise, I do it all before play when I can, and just read off the list. The actual randomness is identical between the two, but one is much faster and smoother in play.
Anyhow, for the second type, direct references from one table to another are death. You want to either use only one at a time, or set it up so that you can roll all the relevant tables with a fistful of dice simultaneously. For example, my potion tables are intentionally written on loose sheets of paper that can be laid out, and when I roll on them, I roll all the dice at once, and just treat the dice corresponding in the system of leftmost die to topmost table and then progressing rightward and downward.
Based on the potion tables and my experience with them, I would recommend doing one of two things in terms of designing the tables.
1) Make them all different die types so the correspondence is obvious.
2) Make them all the same dice type so that the correspondence is more or less irrelevant.
The advantage of being able to roll simultaneously is to maintain that compression of emotion, so that only the announcement phase is stretched out, and then only slightly, and one can do tricks like read them off from best result to worst, or least interesting to most, so that there's a flow in this phase that keeps things moving instead of bogging things down.
I'd also recommend not using percentile tables for this second type of random table unless you have colour coded sets of percentile dice, because otherwise the time spent sorting them into pairs abolishes the time savings of rolling simultaneously.
The presence of "Roll x times on table y" on so many tables suggests that people value the capability of a table to generate multiple results from itself, but I think this is an inefficient method of achieving this result, since it necessarily forces one back to sequential rolling.I would suggest that if one wants to vary the number of results one gets from a table as well as the actual results, a dice map like my ones for nomad families and gear would be more suitable.
On a final note, I think random tables should be fairly scarce in actual play. The more random tables you use, the more they lose their effect and the less meaningful PC choice becomes. As well, unless you're rolling on them before play, it becomes hard to supply information about the possible outcomes beforehand, which leaves PCs without the information they need to make meaningful choices. In fact, this is one of the useful effects of random tables - to suddenly and briefly strip agency from the PCs and referee and place it into the hands of chance. Overused, this becomes boring and frustrating for the PCs, and disorienting for the referee, though in small doses it varies the level of control the PCs have, which exacerbates their feelings of imperilment.