Australia

A few things come to mind, with the caveat of course this is all from a layman's perspective and may be misinformed, dumb, or otherwise not feasible.

Basic stuff:

• More frequent services. Aside from the sardine tins they can become during peak times, lengthy waits, particularly in bad weather, aren't great. It also softens the blow if there's a service fault (only a few minutes until the next one comes by).
• Disincentivise service cancellations, a late service is better than one that doesn't run at all. It won't always be possible to avoid cancelling, but I'm told the cancellation penalty can be less severe than the punctuality one.
• Chain/rework service SLAs with an "overall service" goal. It's frustrating when your service has been delayed, and the connecting service you would have caught leaves empty but on time to meet their own timeliness metrics.
• Perhaps linked to that, I have to wonder how wise it is to contract these things out. Not sure what the answer is as having it all be govt-run doesn't fill me with optimism either, maybe rethinking how contracts are written and awarded needs a rethink - but moving the focus from serving the public need to minimising cost/maximising profit cannot possibly be in the best interests of the commuter.

More ambitious:

• There need to be trains that go between the existing lines, concentric circles around the city essentially. To visit a friend who lives only about 15km from me, using PT the train-only option involves travelling into the city, swapping trains, then travelling out of the city on his line. It's over 2 hours of travel. Adding buses brings that down to about 75-80 mins. Driving there takes me 20.
• Smarter express services that make a meaningful difference to trip times. Eg buses where the pickup/dropoff stops are preset (bookable?), maybe even dynamic routes based on the stops required? Dunno, this is a tough one but on my commute the current "express" option saves only 3 minutes lol.
• More separated roadways for buses, so they are less at the mercy of other traffic. That has the added benefit of reducing the volume of that other traffic, so things get better for both PT and private vehicles.
• More 3+ line rails, to allow for passing. That would reduce the flow-on impacts of delays to a service, and would allow for more express services that don't have to accommodate catching an all-stops one.
• Better start-of-trip options. Park and ride sounds good but they are always packed, and are basically just a shopping centre for car thieves who know the owners will likely not be back until 5pm or so. We've already lost one car this way, insured but it was a massive headache. Airport-style shuttle buses perhaps? Something that might allow a pushbike to be transported too, as that might help with the last-km issues.
• More of a societal thing than being PT-specific, but move away from the "one big CBD" model. Everybody wanting to converge on more or less the same point puts a huge amount of concentrated pressure on a system. That system has to be designed and funded to accommodate these enormous peaks, but will be massive overkill at other times. Distributing the destinations reduces that concentration, but also helps to justify better services in areas that everyone currently leaves because they have to go to the city instead.

There are no doubt tons of others but that's a start.