To find out about the "problems" of the 6.5 Mannlicher, both 6.5x53R Mannlicher and the rimless 6.5x54 M-Sch, we have to go back to the early 1890s ballistic habits. At that time European cartridge designers still thought along the lines of black powder and lead bullets.
As the early small bore bullets were rather thin-jacketed and -by today's standards- long and heavy for the caliber, and the early smokeless powders were fast burning, designers tended to use slightly undersize bullets and relied on the "slugging up" of the bullets on the sudden blow of pressure to fill the grooves. FI, this idea worked with the original 8x57 227gr .318" bullet to fill the .324" grooves, but not with lighter and stronger bullets. This lead to the confusion with .318" and .324" 8mm bullets.
The designer of the 6.5mm Mannlicher cartridges followed the same path of relying on "slugging up". On this forum you often read complains on the "outsize" groove diameter of Mannlicher-Schoenauer 6.5 mm barrels. If you take a look into the European CIP proof tables, you will find a minimum groove diameter of 6.78mm = surprise! .2669", the minimum bore diameter is 6.48mm = .255", so the minimum barrel diameters are both .03mm = .0012" wider than prescribed for the other 6.5mm cartridges like 6.5x55, 6.5x57, 6.5x68.
The maximum bullet diameter is the same for these "6.5mm" cartridges, 6.70mm = .264".
For the sake of "science" I have torn apart some original cartridges and miked the bullets:
Hornady 160gr round nose: .264"
1928 Portuguese military 158gr fmj/solid round nose: .263"
RWS, both pre- and post-WW2 make, 159gr TMR/round nose soft point: .261"!
RWS 159gr prewar H-jacketed boat-tail hollow-point .261" also.
Apparently most Mannlicher-Schoenauers did not shoot too bad with these "grossly undersized" bullets. So I dare to recommend for old M-Sch rifles:
do not try light bullets below 140gr
do not try hard bullets like Noslers or even homogenous bullets.
As M1903 Mannlicher-Schoenauer magazines, other than the post-war models, guide the cartridges at the base and at the bullet tip, feeding is most reliable with round noses seated to maximum cartridge length.