One of these may have somethig to do with your first problem where some leds are on with no input.
Application Hints
Three of the most commonly needed precautions for using
the LM3914 are shown in the first typical application drawing
showing a 0V–5V bar graph meter. The most difficult problem
occurs when large LED currents are being drawn, especially
in bar graph mode. These currents flowing out of the
ground pin cause voltage drops in external wiring, and thus
errors and oscillations. Bringing the return wires from signal
sources, reference ground and bottom of the resistor string
(as illustrated) to a single point very near pin 2 is the best
solution.
Long wires from VLED to LED anode common can cause
oscillations. Depending on the severity of the problem
0.05μF to 2.2μF decoupling capacitors from LED anode
common to pin 2 will damp the circuit. If LED anode line
wiring is inaccessible, often similar decoupling from pin 1 to
pin 2 will be sufficient.
If LED turn ON seems slow (bar mode) or several LEDs light
(dot mode), oscillation or excessive noise is usually the
problem. In cases where proper wiring and bypassing fail to
stop oscillations, V+ voltage at pin 3 is usually below suggested
limits. Expanded scale meter applications may have
one or both ends of the internal voltage divider terminated at
relatively high value resistors. These high-impedance ends
should be bypassed to pin 2 with at least a 0.001μF capacitor,
or up to 0.1μF in noisy environment.