Can sampling I2C influence transmission?
It looks like you're getting some crosstalk between your signals. In your first example, the falling edge of the SDA line is also coupling briefly into the SCK line. In the second example, there may be some other signal coupling into the SDA line.

In order to debug this, you need to switch to an oscilloscope that can show you the analog voltage waveform of these glitches. Preferably one with multiple channels, so that you can simultaneously probe physically adjacent signals and find the correlation between edges and glitches.

Keep in mind that a glitch seen on the logic analyzer may or may not be interpreted as a glitch by the other logic on your board. Also, there may be other glitches that the analyzer isn't picking up, but they are affecting the logic.