Have a 2005 f150 4.6L 4x2 with fault trans message and blinking o/d. Got code p0720, wires look fine replaced sensor. 1,2 slow on grabbing the gear, must be in a safety mode. 3,4 gears work good.

Follow the links for each fault code.
http://www.obd-codes.com/p0500
P0700 Transmission Control System Malfunction
P0720 Output Speed Sensor Circuit Malfunction
P0715 sets when there is an error in the transmission's input speed sensor signal. On the front of the trans there is an input and output speed sensor that the trans controller looks at for shifting control.

While the code could have set because of a wiring or connection problem, it's almost surely the sensor. Input speed sensor failures are not uncommon.

The input speed sensor is mounted right on the front of the trans directly under where the cooler lines attach. It threads directly in and has a 1" hex for a socket for removal. If the wiring and connection look visibly ok then I would recommend replacing the sensor

P0700 Transmission control system malfunction
P0720 output speed sensor circuit malfunction
P0731 gear ratio error in first gear
P0732 gear ratio error in second gear

No --- it just needs the TCM checked out as that is indicated by the series of faults.

code p0720 refers to out put shaft speed (OSS) sensor-circuit malfunction===causes wiring OSS sensor --ECM/TCM
Having replace both sensors means that you still not have fixed the fault. Check the wiring and connectors for moisture an damaged pins and the TCM plays a big part in your problem ( transmission control module)

code p0720 refers to output shaft speed sensor(OSS)--circuit malfunction====causes--wiring--OSS sensor--ECM/TCM
of it has just happened check the wiring and connections to the transmission for water and corrosion or replace the OSS sensor in the transmission.

2001 grand cherokee?
nor years of all parts swapped.
swaps are super complex topics, endless possibles.

dont expect magic from any TCM.
they cant tell you ever possible way things can be wrong
it will fail to shift right if things are wrong,
the trans TCM can go to limphome mode, read the service manual chapter 21 yet its free, posted here 300 times.
forget the silly engine , light (CEL) use only a scan tool one that can read all factory codes not some $20 tool.
CEL lamp is for failing smog. only. never trust it, if out.

i say bad shift solinoids.
the TCM can see late shift error.s but maybe not all.
stick in 1st is a hard failure.
all inputs to the TCM must be correct for the shift to 2nd happens.
check all inputs.
if those are then see if the TCM did shift to 2nd, but the solenoids ignored the logic inputs to the solenoids.
solenoids have many failure mods
dead. (stuck closed)
stuck open, valve open.
or leaking. (leaking can cause stuck in 1st and confuse any TCM)

leaking means breached, valve leaks where it must not. ever.

code p 0500 is for the vehicle speed sensor (VSS) which works the speedo as well as the ratio changes
code p0720 refers to the output shaft sensor --ECM or transmission control module (TCM)
the vss reports to the tcm which reads the road speed and gear ratio and shifts the appropriate solenoid

p0720-- auto. trans. vehicle speed sensor (revolution sensor)

p1574--automatic speed control device/vehicle speed sensor

p0420--two way catalyst system bank 1

P1529 indicates that your TCM asked the ECM to turn on the check engine lamp.

The range switch and the output speed sensors are the items that are abnormally affecting the operation of the transmission. The diagnostic logic in your computer can distinguish these issues from one another, so you'll definitely want to do both. You have no diagnostic code for the input speed sensor (P0715) listed, so I have made no recommendation to replace it. In my opinion, it's not a labor-intensive repair, so I wouldn't recommend replacing it unless you have reason to believe it's bad.

DTC - P0720 (OUTPUT SHAFT SPEED SENSOR SYSTEM)
Code No. P0720 Output shaft speed sensor system
If the output from the output shaft speed sensor is continuously 50% lower than the vehicle speed for 1 second or more while driving in 3rd or 4th gear at a speed of 30 km/h or more, it is judged to be an open circuit or short-circuit in the output shaft speed sensor and diagnostic trouble code No. P0720 is output. If diagnostic trouble code No. P0720 is output four times, the transmission is locked into 3rd gear or 2rid gear as a fail-safe measure.
Probable cause
Malfunction of the output shaft speed sensor
Malfunction of the transfer drive gear or driven gear
Malfunction of connector
Malfunction of the TCM

DTC - P0715 (INPUT SHAFT SPEED SENSOR SYSTEM)
Code No. P0715 input shaft speed sensor system
If no output pulse is detected from the input shaft speed sensor for 1 second or more while driving in 3rd or 4th gear at a speed of 30 km/h (19 mph) or more, it is judged to be an open circuit or short-circuit in the input shaft speed sensor and diagnostic trouble code No. P0715 is output. If diagnostic trouble code P0715 is output four times, the transaxle is locked into 3rd gear or 2nd gear as a fail-safe measure.
Probable cause
Malfunction of the input shaft speed sensor
Malfunction of the underdrive clutch retainer
Malfunction of connector
Malfunction of the TCM

Is needed replace.

The P0300 is down to a cylinder misfire, usually it will have a number like 0302 where the 2 would mean the misfire is in number 2 cylinder. When were the plugs and wires last changed? what milage is on the vehicle?
P0720 is the output shaft speed sensor seems to be more of a common problem on the older hyundai's, is the gear change smooth or erratic? has it ever locked itself into gear? if you clear these codes how quickly do they come back?