AgNO3 is sensitive to light. Ultraviolet light of a certain range of wavelengths reduces it to Ag; therefore, the molarity of the solution changes. Remember that Ag salts are one of the light sensitive materials in paper photography.
You don't want Ag2O (the end product of the formation of AgOH) to form but that will happen in basic solution.
Excess SCN^- can form a complex ion with Ag^+ so the idea is to minimize the concentration of SCN^-.
These may not be the only reasons for #2 and #3; i.e., there may be others.
why is it necessary to store AgNO3 solution in an amber bottle?
Why must volhard titration be carried out in strongly acidic medium?
Why is titration of AgNO3 with KSCN be done with vigorous swirling?
2 answers
The low pH is needed to prevent the Fe^+3(aq) indicator from hydrolyzing (forming hydroxy complexes and eventually iron(III) hydroxide). If the ferric salt indicator is altered, there is no clear end point during the titration.