I'd consider my hemi reliable... it's definitely not "unreliable".
Clarky covered the common WH quirks/issues.
Like he says the only major thing you'll find about the 5.7 hemi itself is the valve seat failures. There's enough reports on different forums and info from a few mopar tuners to be pretty-sure there's something happening, but considering the engine is in a crapload of cars, I'm not too nervous about it.
The info suggest it's related to heat-soak in the head after shutdown, which was a common issue in the old-days before retained valve seats... the hemi doesn't have retained valve seats, so it makes sense.
It shouldn't be a problem as-long as you avoid shutting down when hot then cranking it shortly afterwards. Such as fanging it hard to the servo and filling up. I try to let it idle for a couple of minutes before shutting down, and tend to spend a while filling-up an aux tank + main tank.
I've also put a thermo fan with a timer, which has reduced heat-soak slightly, and have an electric bypass water pump to install when I get a chance, to keep coolant circulating for a few minutes after shutting down. The yamaha V8 in our Volvo does that and stays cooler after shutting down, it's a much more refined engine too, so figure there's probably a good reason they did it.
The 545rfe transmission in the hemi is rated for higher torque in the RAM pickups, and seems pretty bullet-proof.
My WH is only used for travelling/touring, and an occasional run to the shops when it's been sitting too long. Never been worried about taking it into the middle of nowhere.
Only engine/trans-related issues have been a failed/jammed EGR valve, failed oil pressure sender and a flooded fuel vapour canister, never prevented from driving though.
Most engine codes (like the EGR valve and oil pressure sender.) cause the MDS to be disabled, which can mean your fuel consumption takes a hit.
The flood fuel vapour canister is a funny one. Basically if you overfill the tank and it floods the canister, it'll stall a few seconds after starting (when the vapour recovery system opens.). Fix is to just drain the canister or wait for the excess fuel to evaporate.
Not sure how likely it is with just the stock fuel tank. I've done it a couple of times when I've filled the aux tank to the top of the filler then parked on an angle. Just due to how the aux tank overflow is plumbed.
Stock with correct engine oil and MDS working propertly should get around ~11-12L/100 cruising, maybe 10L/100 at 90km/hr haha, and ~13-14L/100 around town.
I have a 50mm lift, boxes on the roof and around ~350kg of gear, and with MDS disabled and 31" highway tyres atm I'm getting about 16-17L/100 around town being fairly light on the pedal. With 32-33" muds it'd get around 18L/100 without MDS.
MDS is great on long trips if you 'play' the system a bit. For example, sometimes sitting at 102km/hr could put you at say 14L/100, where-as 100km/hr might let MDS kick-in for longer and the torque converter lock and get you down to like 8L/100. Something to do when you're driving in a straight line for 8 hours too