"Weak" implementation of AES-CTR? Assume an instantiation of AES-CTR like in the following picture:



Some details on the input-values for keystream generation:


COUNT: a 32-bit value associated with the transmission mode
IV#1: a 5-bit value that can be assumed constant for a specified transmission 
IV#2: a 1-bit value indicating the direction of the transmission
incr: a 64-bit value initialized to 0 and then incremented per standard $\bmod 2^{64}$ increment function. 
cipher key: refers to ciphering key which is obviously not known


Assume that all those input values are not difficult to identify/guess as they are required to establish correct transmission and synchronization between the two communicating parties (e.g., direction, radio info, etc). We also assume that no pairs of ciphering keys and input values ($COUNT||IV\#1||IV\#2||0^{26}||incr$) are used. Is this a weak AES-CTR implementation, assuming one can obtain pairs of keystreams/input-values?

I guess we can say this implementation is malleable as any AES-CTR without authentication steps. Any other weaknesses?
If the implementation ensures that no (COUNT, IV#1, IV#2) tuple can ever be used more than once, and if no tuple is ever used to generate more than 264+4 bytes of keystream output, then this scheme is as secure as any instantiation of AES-CTR can be.  Of course, as CTR is not an authenticated encryption mode, it will still be malleable unless combined with a MAC.

Conversely, if an attacker can cause two plaintexts to be encrypted with the same COUNT, IV#1 and IV#2 values, then they can easily obtain the bitwise XOR of the plaintexts, which may be sufficient to at least partially recover the plaintexts themselves.  In particular, if an attacker can cause a plaintext of their choosing (or at least known to them) to be encrypted with a chosen COUNT, IV#1 and IV#2, then they can fully decrypt any other plaintext (of equal or lower length) encrypted with those same values.

Your question does not contain enough information to let us tell which of these two scenarios applies, and so we cannot say whether this specific AES-CTR instantation is secure (in the usual IND-CPA sense one would expect of CTR mode) or not.

That said, the short length of IV#1 certainly raises some concern.  You have not described exactly what constitutes a single "transmission" in this protocol, but whatever it is, there can be only 32 of them in this scheme before you'd need to rekey (assuming that nothing prevents two transmissions from using the same COUNT values).  That seems like it might be a problem.