How can I measure maximum range of my ohm meter?
Your resolution of the ADC (the analogRead) will be 1/1024 * 5V (since you get a reading in the range 0 to 1023), that is, you can tell the difference in increments of 5/1024 which is 0.00488V, so say roughly 0.005V.
Now, I wrote a little bit of code to work out the voltages that you would get with various values for your varying resistor:
r1 =      0, v = 5.000
r1 =    100, v = 4.545
r1 =    200, v = 4.167
r1 =    300, v = 3.846
r1 =    400, v = 3.571
r1 =    500, v = 3.333
r1 =    600, v = 3.125
r1 =    700, v = 2.941
r1 =    800, v = 2.778
r1 =    900, v = 2.632
r1 =   1000, v = 2.500
r1 =   1100, v = 2.381
r1 =   1200, v = 2.273
r1 =   1300, v = 2.174
r1 =   1400, v = 2.083
r1 =   1500, v = 2.000
r1 =   1600, v = 1.923
r1 =   1700, v = 1.852
r1 =   1800, v = 1.786
r1 =   1900, v = 1.724
r1 =   2000, v = 1.667
r1 =   3000, v = 1.250
r1 =   4000, v = 1.000
r1 =   5000, v = 0.833
r1 =   6000, v = 0.714
r1 =   7000, v = 0.625
r1 =   8000, v = 0.556
r1 =   9000, v = 0.500
r1 =  10000, v = 0.455
r1 =  20000, v = 0.238
r1 =  30000, v = 0.161
r1 =  40000, v = 0.122
r1 =  50000, v = 0.098
r1 =  60000, v = 0.082
r1 =  70000, v = 0.070
r1 =  80000, v = 0.062
r1 =  90000, v = 0.055
r1 = 100000, v = 0.050
r1 = 110000, v = 0.045
r1 = 120000, v = 0.041
r1 = 130000, v = 0.038
r1 = 140000, v = 0.035
r1 = 150000, v = 0.033
r1 = 160000, v = 0.031
r1 = 170000, v = 0.029
r1 = 180000, v = 0.028
r1 = 190000, v = 0.026
r1 = 200000, v = 0.025
r1 = 210000, v = 0.024
r1 = 220000, v = 0.023
r1 = 230000, v = 0.022
r1 = 240000, v = 0.021
r1 = 250000, v = 0.020
r1 = 260000, v = 0.019
r1 = 270000, v = 0.018
r1 = 280000, v = 0.018
r1 = 290000, v = 0.017
r1 = 300000, v = 0.017

You can see that the difference in voltage is only 0.005V (the ADC resolution) between r1 of 90k and 100k. Further down, you can't tell the difference (within 0.005V) of 270k and 300k.
I'm not sure how to express that as an error percentage, perhaps someone better at maths than me can do that. :)